Proximal Policy Optimization

Battery energy storage system (BESS) dispatch must preserve operational feasibility while declining price spreads reduce the margin available to pay for cycling. We study a proximal policy optimization (PPO) controller whose pre-selection physical action mask and emergency projection are separated from a causal, forecast-informed economic advisory. All forecast-dependent methods receive the same causal 24-step forecast and grid-side settlement. Across five PPO seeds, advice-on net profit is 30.59 and 18.04 USD per 336-hour T1 and T2 window, versus 36.77 and 22.94 USD for proxy-cost MPC; PPO remains below this reference in both periods. Advice raises T2 profit from 16.45 to 18.04 USD while reducing throughput, but is immaterial in T1. On disjoint weekly blocks, PPO is stable under daily, weekly, and blended seasonal forecasts, weakens under persistence, and remains below proxy-cost MPC. Paired diagnostics localize changes to the observed 5-10 USD/MWh regime with mixed SoC-dependent effects. An M0-M6 ablation shows that mask removal sends thousands of infeasible requests to projection, while removing both physical layers exposes ramp violations. The evidence separates economic screening from feasibility enforcement without claiming formal safety, lifecycle-optimal aging, or RL dominance.

In reinforcement learning for large language models, Proximal Policy Optimization (PPO) commonly uses a critic to estimate state values and reduce the variance of policy updates. However, we uncover a systematic failure mode in PPO critics, which we call Value Flattening: state values, estimated from multiple Monte Carlo continuations, change sharply across intermediate states while critic predictions remain comparatively flat. We further observe this phenomenon in a controlled FrozenLake environment and find that it becomes more pronounced as the state space grows. Our theoretical and empirical analyses relate Value Flattening to an implicit variance penalty in the critic loss and redundant updates from temporally correlated states with similar gradients. Motivated by these findings, we introduce SParse Proximal Policy Optimization (SP$^3$O), which applies the value loss to only a few well-separated states in each response to mitigate both effects. Experiments on Qwen3-Base show that SP$^3$O with only three states supervised per response can mitigate Value Flattening and consistently improve the learned policy across model sizes and evaluation suites. Together, our results identify Value Flattening as an important yet overlooked failure mode of critic learning in standard PPO and show that a simple sparse supervision strategy can mitigate it.

Wireless edge caching networks typically consist of many independent Base Stations (BSs), each facing its own request rate and content popularity profile. Training a Reinforcement Learning (RL) caching agent from scratch at every BS forces each agent to relearn, through slow trial and error, a decision problem that is structurally identical across the network. Meta-reinforcement learning removes this redundancy by learning a shared initialization that adapts to any BS in a few local updates; however, meta-training itself becomes the bottleneck at scale: the meta-gradient must be estimated from a small subset of BSs at each meta-iteration, and sampling this subset uniformly at random yields a high-variance estimate, an issue existing meta-RL caching frameworks leave unaddressed. This paper proposes a meta-reinforcement learning framework for caching across independent, non-overlapping BSs that directly targets this bottleneck. Each BS runs a local Proximal Policy Optimization (PPO) agent, formulated as a Semi-Markov Decision Process (SMDP) over content popularity, size, lifetime, and importance, while a shared meta-policy is learned via a Model-Agnostic Meta-Learning (MAML)-style loop. To scale meta-training and accelerate convergence, we introduce gradient-based clustering, which groups BSs by local gradient similarity and draws from every cluster, in proportion to its size, at each meta-iteration. We prove, via an Analysis of Variance (ANOVA)-style decomposition of gradient variance, that this strategy yields a strictly lower-variance meta-gradient estimator than uniform random sampling under BS heterogeneity.

Combining aerial thrust with spring-loaded hopping makes monopedal quadcopters promising for locomotion over complex terrain, but heuristic proportional-integral-derivative (PID) tuning limits coordination between active thrust and passive contact dynamics. We present a direct estimated-state-to-motor Proximal Policy Optimization (PPO) policy that commands four motors without an explicit hopping state machine or low-level attitude PID. Its reward combines Energy-Manifold Shaping for mass-normalized vertical-energy tracking and apex-state anchoring with Efficiency Shaping, which uses a history-aware power estimator to penalize general power use, impose an additional airborne-power cost, and penalize airborne near-stationarity. In representative hardware runs, the PPO-based control stack reduced cycle-averaged measured electrical power by 30.7% and mean total normalized thrust by 49.8% relative to the tuned PID-based control stack, while retaining repeatable commanded-height hopping and more concentrated landings. These observations are consistent with improved use of passive dynamics and reduced measured electrical demand.

Existing post-training pipelines for coding and terminal agents suffer severe token and control fidelity errors: simplified training environments mismatch production deployments, and offline token reconstruction from agent logs distorts original prompts and conflates policy calls with background model operations. We present a fidelity-aware training coupling framework that retains trainer-side sampling over original prompts, eliminates spurious model calls via a negotiated training protocol, and restricts loss computation to verifiable token spans with closed-failure guarantees. We further propose Certified Divergence Proximal Policy Optimization (C-DPPO), which establishes tight two-sided TV certification bounds, adaptive-K rules, budget-aware sequence guarantees, and error-robust policy masking atop standard DPPO. Evaluated on matched Baize5B and Baize10B models with identical training and test protocols on TMax-100, C-DPPO yields a consistent +3.0-point performance gain over standard DPPO across model scales. Certificate audits validate the reliability and full operational coverage of our certified training pipeline.

We study the allocation of indivisible goods among agents with identical additive valuations, focusing on envy-freeness up to one good (EF1) and Nash social welfare (NSW). Since every maximum-NSW allocation is EF1 under additive valuations, the associated threshold problem inherits the known strong NP-hardness of NSW maximization under identical additive valuations and is strongly NP-complete. We therefore focus on welfare guarantees satisfied by arbitrary EF1 allocations. Although every such allocation is known to achieve an $e^{-1/e}$-approximation to the unrestricted optimal NSW, we identify conditions yielding stronger guarantees. Under uniform valuations, every EF1 allocation is NSW-optimal. Under an $\varepsilon$-small-item condition, every EF1 allocation achieves an explicit approximation ratio $ρ_n(\varepsilon)$ satisfying $ρ_n(\varepsilon) = 1-O(\varepsilon^2)$ as $\varepsilon\to 0$ for fixed $n$. We further consider the stronger sequential requirement that $\operatorname{EF1}$ be maintained after every item assignment. For this setting, we introduce \emph{PriorityNet}, a deep reinforcement learning framework trained with Proximal Policy Optimization (PPO) and equipped with prospective $\operatorname{EF1}$ action masking, which guarantees prefix-wise $\operatorname{EF1}$ by construction. Across 3,000 test instances in each of the offline full-information and random-order online regimes ($n\in[2,20]$, $m\in[5,100]$), PriorityNet achieves mean normalized $\operatorname{NSW}$ values of $0.9911$ and $0.9701$, respectively. Relative to the offline Longest Processing Time (LPT) heuristic and the online least-valued-bundle rule, it attains instance-wise win-minus-loss rates of $+27.10\%$ and $+17.87\%$. Its aggregate welfare matches the offline LPT baseline to four decimal places and modestly improves upon the online baseline, from $0.9694$ to $0.9701$.

Offline reinforcement learning (RL) must reconcile two competing requirements: policy updates should stay near dataset-supported actions to keep value estimates reliable, yet meaningful gains often require moving beyond the behavior distribution. We develop a geometric view of offline actor updates by modeling policies as a probability manifold endowed with a chosen metric geometry. Under this lens, a broad class of offline actor objectives can be interpreted as a single proximal policy improvement step (SPI), i.e., an implicit discretization of a manifold gradient flow induced by a critic-defined energy. Building on this insight, we propose multi-step proximal policy improvement (MPI), a plug-in refinement mechanism that composes sequential re-centered proximal steps. MPI enables controlled policy improvement beyond dataset support while retaining proximal control at each refinement. The framework accommodates multiple policy geometries and admits practical instantiations for deterministic and diagonal-Gaussian policies. Experiments on D4RL benchmarks show that small numbers of MPI refinements improve strong offline baselines, including TD3+BC, ReBRAC, and IQL, on many tasks. Focused diagnostics further distinguish re-centered refinement from fixed-objective update scheduling and characterize limitations under critic error.

With the rapid development of the Internet of Things, computation intensive directed acyclic graph (DAG) tasks have become increasingly common in cloud-edge-end collaborative environments. However, cloud, edge, and end nodes are highly heterogeneous in computing capacity, network bandwidth, and energy consumption, which makes the efficient scheduling of tasks with complex dependencies an NP-hard problem. Traditional heuristic algorithms and conventional reinforcement-learning methods often fail to capture the spatio-temporal dynamics of system resources. This paper proposes PPO-STGNN, a DAG task-scheduling algorithm that integrates proximal policy optimization (PPO) with spatio-temporal graph neural networks (STGNNs). The method uses an STGNN to extract features from both the DAG task topology and the physical cloud-edge-end resource graph, and then optimizes the scheduling policy through PPO to minimize makespan and schedule length ratio (SLR) while improving CPU and memory load balancing. To accelerate convergence, a multi-teacher behavior-cloning mechanism is introduced for pretraining. Experimental results show that PPO-STGNN significantly improves load balancing while maintaining a low completion time, making it suitable for dynamic and heterogeneous cloud-edge- end DAG scheduling scenarios.

Combining learned policies with model predictive control can leverage learned task priors while retaining online adaptation to new objectives and constraints, but performance degrades when the policy is out of distribution. In policy-guided model predictive path integral (MPPI) control, a policy-centered warm-start approach centers the sampling distribution on the policy output. When the prior is mismatched, centering the sampling distribution on the policy output restricts exploration around an unsuitable solution and prevents recovery toward the task optimum. We propose Proximal Prior Injection (ProxPI), which retains nominal-centered MPPI sampling and incorporates the policy through a soft proximity cost. This matches the in-distribution performance of existing prior-injection schemes while enabling the optimizer to escape an inaccurate policy and recover vanilla MPPI-level performance. We theoretically show that re-centering on the prior discards the optimizer's correction at every update, whereas nominal-centered sampling retains it and converges to a solution set by both the task cost and the prior, and that this failure is not removed by a larger rollout budget. Simulations and real-robot experiments demonstrate robust performance under both in-distribution and out-of-distribution tasks.

Many automobile and mobility companies deploy learned driving policies on embedded computers with limited memory and power. Pruning, knowledge distillation, and quantization are the standard methods to reduce the size and the inference cost of these policies. However, these methods are commonly assessed by aggregate numerical scores, and such scores may not reflect the ability of the policy to drive safely when interacting with other road users. In this study, we propose a stage-wise closed-loop evaluation approach to follow a driving policy through a compression pipeline. We formulate the driving task as a partially observable Markov decision process (POMDP) and train a belief-state policy with proximal policy optimization (PPO) in Gym-Duckietown. We then extract the actor, compress it one stage at a time, and evaluate it on five driving curricula. We show that structured pruning is the stage at which the driving capability is first lost. Meanwhile, distillation improves the pruned actor, but the improvement is limited by its rehearsal data. Integer quantization of the improved actor loses some of the curricula that require the vehicle to stop and then resume. Interestingly, the same procedure on the unpruned actor preserves all five curricula. Our study thus provides an empirical analysis aiming to answer the currently active discussions on how to accept a compressed driving policy, so as to achieve a safe and statistically reliable deployment of automated driving functions.

Expected-cost constraints can still permit rare, high-cost events. Monte Carlo conditional value at risk (CVaR) gradients can be noisy at high confidence, whereas critics that model an outcome distribution add complexity. We propose BCPPO (Bachelier-Inspired Constrained Proximal Policy Optimization), a proximal policy optimization (PPO) method. Separately initialized cost-prediction networks (critics), trained with random sample masks, produce disagreement that marks predictions sensitive to which state-action regions occur in the training data and to critic training. A Bachelier formula for the expected amount above a reference level converts this disagreement into a smooth policy-update penalty. Gradients from this penalty do not alter the critics, so temporal-difference (TD) critic learning is unchanged. A saturation-aware controller adjusts the mean-cost penalty and stops accumulated error from growing while that penalty is clipped. Deployment retains only the policy network. The disagreement penalty is neither a tail-event probability nor a guaranteed error bound, and it provides no safety guarantee. Across 175 runs with shared tasks, costs, budgets, training steps, and evaluation seeds, no comparator attains both higher mean return and lower mean CVaR than BCPPO in any task. On Push1, BCPPO has no lower return and no higher CVaR than every comparator, with at least one strict gain. These results support a practical balance among reward, caution around cost predictions that vary across trained critics, and policy-only deployment.

Collision avoidance systems are commonly used to avoid fragmentation events occurring in Low-Earth Orbit (LEO) and Geosynchronous Equatorial Orbit (GEO). However, these events have been growing in frequency as orbital congestion worsens with the launch of megaconstellations. Consequently, conjunction alerts and collision risks are becoming increasingly common. Current practices, which are commonly manual or rule-based, have difficulty scaling to these worsening dynamic environments. To address this intensifying situation, we propose a reinforcement-learning policy for autonomous collision avoidance, trained via Proximal Policy Optimization (PPO) along with an open-source, high-fidelity astrodynamics simulator for training and evaluation. In 1,000 deterministic GEO episodes, our agent achieves a 97.5% collision avoidance success rate, outperforming traditional controllers such as a rule-based baseline (20.7% success) and an impulsive delta-v planner baseline (27.5% success). To achieve these results, we designed a simulator to train and evaluate our agent, using real-world and simulated debris. We simulate Newtonian two-body dynamics using Sun/Moon third-body perturbations, fuel-dependent thrust, and configurable debris fields. The agent is trained with curriculum learning and shaped rewards oriented toward encouraging survival, adequate projected miss distance, and delta-v conservation. Finally, our evaluation consisted of a fully deterministic pipeline, including shared seeds, per-episode logs, and telemetry exports. Our work is a publicly available framework at https://purl.org/sat-trajectory-avoidance

Preference-based reinforcement learning (PbRL) for general stochastic MDPs often requires training a reward model. Existing reward-model-free methods are either restricted to bandits or deterministic MDPs, such as DPO or P3O, or use zeroth-order, gradient-free optimization, which in general exhibits a slower convergence rate than gradient-based algorithms. Furthermore, existing reward-model-free preference-based RL algorithms almost exclusively use trajectory-level feedback, which can require significant effort from a human evaluator when trajectories are long. On the other hand, segments are much shorter, so they are easier to compare and evaluate. In this paper, we introduce a novel reward-model-free, critic-free, and gradient-based PbRL algorithm compatible with segment preferences named Segment Pairwise Proximal Policy Optimization (SP3O). SP3O utilizes segment-level preference feedback to construct an accurate policy value difference estimator via off-policy importance sampling, and then uses the estimator to compute the policy gradient via a PPO-type loss function. We provide a theoretical basis for the algorithm and analyze the tradeoff in choosing the segment length. We also evaluate it experimentally against other PbRL/RLHF algorithms in robotic control and LLM finetuning settings to show its improved performance, especially in long-horizon tasks.

Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.

Variational Autoencoders are widely used to encode high-dimensional and noisy observations in robotics. However, their stochastic latent creates a mismatch with Proximal Policy Optimization (PPO): an effective policy marginalizes over the latent distribution, whereas former implementations estimate its probability ratio and KL divergence using only one latent sample. We identify a fundamental but overlooked theoretical cause: naive single-sample approximations in stochastic latent space induce significant variance and bias in the surrogate loss. To address this, we introduce P^3 (Probabilistic Policy Propagation), a distribution-aware optimization framework for VAE-based policies. $P^3$ couples moment-based probabilistic method for stable and efficient learning with sampling-based calibration for robust policy behavior under latent uncertainty. In our experiments, P^3 boosts data efficiency from 64.6% to >96%, reduces convergence steps by >20%. Furthermore, P^3 is evaluated on challenging humanoid parkour tasks and shows an effective foundation for VAE-based PPO. Code is available at https://github.com/ylyem9x/P3_Open.

The alignment of Small Language Models (SLMs) in the 70--500M parameter range using reinforcement learning is often considered unstable, though the underlying failure mechanisms have not been systematically investigated. In the State-of-the-Art (SOTA) research, fifteen (model, corpus) configurations were trained using Proximal Policy Optimization (PPO). The experiments included Pythia-70M, 160M, 410M and SmolLM2-135M, 360M on the TinyStories, CNN/DailyMail, and Wikitext-103 corpora. Three reproducible failure modes were identified in small-scale language models: silent LoRA parameter freezing in standard PEFT/TRL pipelines, numerical overflow in importance ratios when using bfloat16, and catastrophic policy collapse due to reward-model error. These issues were addressed using a merge-and-reinitialize adapter technique, float32 precision during PPO updates, and a three-layer safety mechanism comprising reward whitening, importance-ratio guarding, and weight rollback. In this paper, a capacity-headroom hypothesis is proposed, which states that PPO performance at the SLM scale depends on both a fluent supervised model ($\text{PPL}<20$) and a discriminative reward signal, rather than on the number of model parameters. The proposed system converged stably in all experiments and improved preference win rate over the SFT baseline in configurations with a fluent prior and an informative reward signal. Furthermore, it outperformed instruction-tuned baselines while requiring significantly less training data. All checkpoints, preference datasets, and training scripts are publicly released$^§$.

In this work, a quantum architecture search framework for approximate quantum state preparation (QSP) is proposed. QSP is a challenging task, since the search space grows exponentially with the number of qubits, making the identification of the optimal circuit non-trivial. To address this problem, deep reinforcement learning is employed through an agent based on proximal policy optimization. The objective of the agent is to identify the best possible approximation of the target state while simultaneously minimizing the number of gates used. At each step, the agent appends a new gate to the circuit and recomputes the fidelity between the approximated state and the target states. Various experiments have been performed from 2 to 5 qubits. Both predefined states, such as Bell, GHZ, W, and Dicke states, and completely random states are considered. The proposed framework is able to achieve approximation errors of $10^{-14}$.

Multi-drone payload transportation has emerged as a promising research paradigm with potential applications in construction, logistics, and disaster response. However, the complex coupled dynamics among drones, cables, and payloads pose significant challenges, and existing approaches remain limited in safety and scalability, particularly in dynamic and unstructured environments. In this work, we propose a learning-based framework for safe and scalable multi-drone cooperative payload transport. We introduce a minimal 2D abstraction that preserves the task-relevant drone-payload coupling required for coordination and safety, while remaining computationally efficient for large-scale learning. Using domain randomization over team size and physical parameters, we train a fully distributed policy via Discrete Graph Control Barrier Function Proximal Policy Optimization (DGPPO), enabling robust zero-shot sim-to-real transfer without fine-tuning. Extensive real-world evaluations demonstrate that a single learned policy generalizes across varying team sizes and task scenarios. Furthermore, multi-group hardware experiments show that the same policy can safely operate in dynamic environments, where other drone teams act as moving obstacles. These results indicate that the proposed framework enables efficient, safe, and scalable multi-drone payload transportation with strong generalization to complex real-world conditions.

Training reinforcement-learning agents directly on physical robots makes every fall costly, since a fall can damage the platform and cannot be undone like a simulator reset; the goal is therefore to minimize falls during training rather than trade them off against return, as constrained Markov decision process (MDP) formulations do. A standard mitigation hands control to a separate recovery policy whenever the agent leaves a designer-specified safe region (a subset of state space it should stay within), but the resulting mixed-policy rollouts silently bias every on-policy update, and the importance-sampling correction that would remove this bias is ill-defined whenever the recovery policy is deterministic. We address this bias with a drop-in modification of proximal policy optimization (PPO). Its core is an unbiased policy-gradient estimator that uses the score function only at safe timesteps and never evaluates the recovery policy's density, so it stays valid even when the recovery policy is deterministic, exactly where importance sampling breaks, and it empirically dominates importance sampling even when the recovery policy is stochastic. Because the recovery policy still makes credit assignment slow near the safe-region boundary, two further components accelerate learning: a closed-form value for recovery-triggering states when dynamics and recovery are deterministic, and an imitation loss that copies recovery actions only when recovery succeeds. On a three-environment, five-seed benchmark, the resulting algorithm reduces training-time falls by factors of 233x, 48x, and 26x on HalfCheetah, Ant, and Unitree Go1 over standard PPO, while matching or exceeding PPO's final reward, and on Ant, where the recovery policy is unreliable, it is the only method that reaches 80% of the best final reward.

We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity? We cast this as a budget-constrained combinatorial optimization problem on graphs, selecting $k$ edge additions that maximize $s$--$t$ max-flow, a theory-grounded measure of routing capacity, and solve it with graph reinforcement learning. Our lightweight agent combines a message-passing policy network with proximal policy optimization (PPO) and action masking, and is trained under a hub-exclusion curriculum: the network's top hubs are removed from training subgraphs, forcing the policy to learn capacity-aware placement rather than hub attachment. In extensive experiments on real Lightning Network snapshots, our method consistently outperforms strong heuristic baselines on the max-flow objective across multiple seeds and unseen graphs. The agent has been deployed in production for peer recommendations, executing 4640 channel-open decisions that cumulatively allocate 267.3 BTC over $16 million across 30 managed nodes.

Reinforcement learning from human feedback (RLHF) has emerged as a powerful paradigm for aligning generative models with human preferences. However, applying RLHF to diffusion models remains highly feedback inefficient, as existing approaches typically require large amounts of human or reward model evaluations. This limitation reduces the practicality of diffusion RLHF in realworld settings where feedback is the primary bottleneck. In this paper, we propose two complementary strategies that substantially improve the feedback efficiency of diffusion RLHF while preserving generalization to unseen prompts. Our key observation is that reward information in diffusion trajectories is unevenly distributed: not all denoising timesteps or trajectories contribute equally to learning from a reward signal. By emphasizing informative timesteps and trajectories during optimization, we obtain more effective gradient updates. First, we introduce a per-timestep weighting scheme that reweights denoising steps during policy optimization. We theoretically connect this weighting to the optimal convergence properties of proximal policy optimization (PPO) and approximate the resulting weighting trend empirically. Second, we introduce a replay mechanism that prioritizes informative trajectories, enabling the model to reuse past samples instead of repeatedly querying new rewards. Together, these strategies significantly improve the feedback efficiency of diffusion RLHF. Under identical hyperparameter settings, our approach achieves up to a 6$\times$ improvement in sample efficiency compared to widely used diffusion RLHF baselines.

Deep reinforcement learning (DRL) in industrial control often suffers from lag and overshoot due to purely reactive control based on the current tracking error. To achieve anticipatory control without high computational overhead, we introduce a predictive formulation that augments the DRL state space with target velocities and future reference horizons. Evaluating eight configurations using proximal policy optimization (PPO) on a 1-degree-of-freedom (1-DoF) helicopter testbed, simulation results showed a 9-fold error reduction, lowering the mean absolute deviation from 2.73° to 0.31°. However, zero-shot transfer to physical hardware revealed a sim-to-real gap. Interestingly, a simpler configuration using a single, further look-ahead horizon matched the real-world top performance of the most complex model (1.11°). Overall, evaluating various combinations of prediction horizons and target velocities demonstrated that highly granular predictive data is not necessarily required for physical transfer.

Deep reinforcement learning (DRL) offers powerful control for industrial cyber-physical systems (ICPSs), but its "black-box" exploration risks violating strict hardware safety limits. Typically, these constraints are managed through complex reward shaping. In this work-in-progress paper, we embed a differentiable physics model directly into the proximal policy optimization (PPO) actor loss function. By simulating short-horizon future trajectories during training, the policy is penalized for anticipated safety violations independent of the task-reward signal. Evaluated on a simulated 1-degree-of-freedom helicopter testbed with strict pitch constraints, our physics-informed soft regularizations substantially reduce constraint violations while maintaining reliable target tracking.

Reinforcement Learning from Human Feedback (RLHF) for Large Language Models increasingly relies on critic-free methods as a practical alternative to actor--critic training. Despite their simplicity, existing critic-free approaches propagate a trajectory-level learning signal uniformly across all tokens in a trajectory. This requires full-trajectory policy updates for every rollout, leading to substantial optimization cost for long reasoning traces, even though intermediate prefixes often contain enough information to largely determine the final outcome. We propose Prefix-Sampling Proximal Policy Optimization (PS-PPO), a compute-efficient critic-free method for RLHF that exploits this temporal redundancy. PS-PPO introduces a prompt-conditioned cutoff distribution and samples a cutoff timestep for each trajectory. During the update pass, PS-PPO backpropagates only through the sampled prefix of each trajectory and applies an importance-weighting correction so that the resulting truncated gradient estimator remains unbiased with respect to the full-trajectory objective. Experiments on mathematical reasoning and RLHF benchmarks show that PS-PPO achieves large reductions in training compute and peak GPU memory, while maintaining accuracy comparable to strong critic-free baselines.

Reinforcement learning (RL) has emerged as a promising solution to accomplish complex robotic control tasks; however, most of the current work ignores the safety requirements. Safe RL seeks to maximize task performance while satisfying explicit physical constraints, but current algorithms struggle to learn the policy efficiently with precise constraint satisfaction. This work proposes PPO-EAL, a novel first-order constrained policy optimization framework that integrates exact augmented Lagrangian optimization into proximal policy optimization for safe robotic control. By combining clipped policy updates with exact quadratic penalty terms, PPO-EAL achieves theoretically grounded constraint enforcement without requiring impractically large penalty factors. A momentum-regulated multiplier update further improves dual-variable stability, reducing constraint oscillation and unsafe behavior while preserving task performance. We provide exactness and convergence analysis under standard stochastic approximation assumptions. Extensive validation across diverse GPU-accelerated robotic benchmarks-including cart-pole balancing, cart-double-pendulum stabilization, 7-DoF Franka end-effector reaching, and quadrupedal locomotion-demonstrates superior safety precision and reward performance compared with state-of-the-art first-order safe RL baselines. Finally, we demonstrate zero-shot sim-to-real deployment in a contact-rich gear assembly task, where PPO-EAL substantially improves task success, reduces peak contact force, and enhances operational robustness. These results establish PPO-EAL as a general and practically deployable safe RL framework for diverse safety-critical robotic systems.

In actor-critic reinforcement learning, network architectures are typically manually designed. Automating this design is challenging because each candidate must be trained before evaluation, and the design space is open-ended. To address these challenges, we introduce EVOM, an agentic meta-evolution framework for discovering high-performance actor-critic architectures. We frame architecture search as a bi-level optimization: an inner loop trains weights via the low-fidelity proximal policy optimization (PPO), while an outer loop drives meta-evolution by iteratively refining architecture programs. Crucially, this outer loop is powered by an LLM-based design agent that operates purely as an architecture designer, completely decoupled from policy execution and environment control. Experiments reveal that EVOM outperforms the manually designed baseline, an LLM-guided random search, and the state-of-the-art LLM-guided programmatic policy search method MLES, delivering superior performance on Ant-v4 and HalfCheetah-v4. Ablation studies validate that both the meta-evolution loop and the LLM Design Agent are indispensable for final performance.

Proximal Policy Optimization (PPO) is the standard policy-gradient algorithm for on-policy reinforcement learning. The literature presents it in two forms, a clipped surrogate that bounds the importance ratio between successive policies and a Kullback-Leibler penalty between them. These forms are treated as separate algorithms with their own gradients, their own hyperparameters, and their own reference implementations, and a sizeable body of empirical work compares them. We show that the gradient of the clipped surrogate is reproduced exactly by a Kullback-Leibler surrogate whose coefficient varies per sample, with closed-form dependence on the importance ratio and the advantage. The identity holds at every minibatch step and across the entire inner loop, and on five MuJoCo continuous-control benchmarks the two losses produce indistinguishable training curves. The reformulation exposes a structural feature of the clipped surrogate that the min notation hides. PPO-Clip's implicit per-sample penalty is a step function at the boundary of the trust region, and the shape of this coefficient is the natural design axis for generalising the algorithm. We sketch the resulting follow-up directions in the discussion.

Knowledge distillation transfers a teacher's competence to a small student but is brittle in the small-student regime: forcing the student to imitate logits from a much larger teacher hurts generalization on benchmark families beyond the training corpus. Reinforcement learning (RL) avoids logit imitation by training on the student's own rollouts. However, on questions where every rollout fails - yielding zero advantage and being silently discarded - injecting a stronger teacher's response into the policy gradient breaks the on-policy assumption and induces drift. We introduce Zone of Proximal Policy Optimization (ZPPO), inspired by Vygotsky's zone of proximal development. ZPPO keeps the teacher inside the prompt rather than the policy gradient. On hard questions, where the student's mean rollout accuracy is below half, ZPPO constructs two reformulated prompts. A Binary Candidate-included Question (BCQ) pairs one correct teacher response with one incorrect student response as anonymized candidates the student uses as references. A Negative Candidate-included Question (NCQ) aggregates the student's wrong rollouts into a single prompt to surface their shared failure modes. A prompt replay buffer recirculates each hard question until it either graduates - the student's mean rollout accuracy on it reaches half or more - or is FIFO-evicted under finite capacity, amplifying BCQ and NCQ inside the student's current zone of proximal development. We post-train Qwen3.5 students at four scales (0.8B-9B) as vision-language models with a 27B teacher and evaluate them on a 31-benchmark suite (16 VLM, 10 LLM, 5 Video); ZPPO outperforms off/on-policy distillation and GRPO, with the largest gains at the smallest scale.

This paper explores policy gradient algorithms for training stochastic policies to sample from structured discrete probability distributions under the Generative Flow Network (GFlowNet) framework. Building on extensive theoretical connections between GFlowNets and entropy-regularized reinforcement learning, we derive equivalents of standard policy gradient algorithms for training GFlowNets, as well as experimentally explore their various methodological aspects, including baseline training and advantage estimation. Most importantly, our work is the first to derive and successfully apply proximal policy optimization to GFlowNets, showing its improved convergence speed and data efficiency compared to standard GFlowNet training objectives on benchmarks ranging from synthetic energies to molecular graph generation.

Recent work has demonstrated that online reinforcement learning (RL) can substantially improve the quality and alignment of flow matching models for image and video generation. Methods such as Flow-GRPO and CPS cast the denoising process as a Markov Decision Process and apply PPO-style ratio clipping to enforce a trust region. However, we argue that ratio clipping is structurally ill-suited for flow models: the probability ratio between new and old policies is a noisy, single-sample estimate of the true policy divergence, leading to over-constraining in some regions of the trajectory and under-constraining in others. We propose Flow-DPPO (Flow Divergence Proximal Policy Optimization), which replaces ratio clipping with a divergence proximal constraint. A key observation is that the per-step policy in flow models is Gaussian, enabling exact and cheap computation of the KL divergence between old and new policies. Flow-DPPO employs an asymmetric divergence mask that blocks gradient updates only when they simultaneously move away from the trusted region and violate the divergence threshold. Experiments show that Flow-DPPO achieves higher rewards with better KL-proximal efficiency, alleviates catastrophic forgetting, promotes balanced multi-objective optimization, and enables stable multi-epoch training where ratio clipping degrades. Code and models are available at https://github.com/Tencent-Hunyuan/UniRL/tree/main/FlowDPPO.

The rapid evolution of financial technology demands sophisticated artificial intelligence systems capable of handling diverse challenges across multiple domains simultaneously. This paper presents a groundbreaking unified framework that seamlessly integrates Proximal Policy Optimization for robo-advisory systems, advanced time-series prediction models for high-frequency trading, in-context learning mechanisms for dynamic investment advisory, game-theoretic approaches for competitive banking scenarios, and unified embeddings for cross-modal financial sentiment analysis. Our comprehensive framework addresses the critical gap in existing literature where these technologies have been developed in isolation, failing to leverage their synergistic potential. Through extensive experimentation across multiple financial datasets and real-world scenarios, we demonstrate that our integrated approach achieves superior performance compared to specialized single-domain systems. Specifically, our framework shows a 23.7% improvement in portfolio optimization metrics, reduces prediction error in high-frequency trading by 31.2%, enhances investment recommendation accuracy by 18.9%, optimizes competitive banking strategies with a 27.4% increase in Nash equilibrium convergence speed, and improves sentiment analysis accuracy by 15.6% through cross-modal fusion. The theoretical foundation of our work establishes convergence guarantees for the integrated optimization problem, while our empirical results validate the practical applicability across diverse financial institutions. This research not only advances the state-of-the-art in financial AI but also provides a blueprint for developing comprehensive intelligent systems that can adapt to the complex, interconnected nature of modern financial markets.

Reinforcement Learning from Human Feedback via Proximal Policy Optimization often suffers from policy mode collapse, brittle exploration loops, and distribution drift. This paper introduces Variational Proximal Policy Optimization ($\textsc{VP}_2\textsc{O}$), a particle-based variational inference framework that maps policy optimization to Stein Variational Gradient Descent within a Mixture-of-Experts architecture. By leveraging functional kernels over localized expert prototypes alongside an expert orthogonalization loss, $\textsc{VP}_2\textsc{O}$ introduces a geometry-based proximal-control mechanism that can reduce reliance on fixed clipping or KL schedules. Our results on a 33B/4B sparse Mixture-of-Experts model show several improvements across complex reasoning benchmarks, establishing a $+\mathbf{179}$ ELO gain on Codeforces and a $\mathbf{32\%}$ reduction in token count on AIME mathematical reasoning tasks.

While Proximal Policy Optimization (PPO) demonstrates strong performance in stationary settings, we show that its standard optimization paradigm struggles in continual and non-stationary environments. The failure does not stem from insufficient model capacity or overly restrictive clipping. Instead, PPO performs persistent, directionally inefficient local updates, which indicates a lack of geometry-aware guidance for accumulating meaningful behavioral change and ultimately hindering transitions toward new behavior patterns. Although divergence-based regularization introduces partial geometric awareness, its monotonically increasing penalties implicitly discourage large policy deviations, even when such shifts are necessary for effective adaptation. To address this limitation, we propose Gaussian Trust Region Policy Optimization (GTR), which reshapes the trust region using a Gaussian kernel. The resulting constraint is bounded and non-monotonic, providing strong local stability while progressively relaxing under sustained high-advantage updates. To further improve robustness, we introduce a Mixture Gaussian Anchor that adapts to recent policy trajectories, reducing variance induced by stale references. GTR is architecture-agnostic and achieves strong performance across games, simulated robotic control, open-world exploration, and language model post-training. These results demonstrate that geometry-aware trust-region design can be a promising direction for robust reinforcement learning in complex non-stationary environments. Our code is available at https://anonymous.4open.science/r/GTR_demo/README.md.

This paper investigates the optimization mechanisms of non-convex Model Predictive Control (MPC) using the Maximum Entropy Differential Dynamic Programming (ME-DDP) framework. Navigating non-convex cost landscapes induced by nonlinear dynamics, multiple obstacles, etc. remains a fundamental challenge in robotics, where gradient-based methods frequently converge to suboptimal local minima. We demonstrate a dual-step optimization mechanism designed to overcome these traps. (1) an initial phase of using DDP to exploit the gradient of the cost landscape, followed by (2) disruption of the optimization via sampling from policies characterized by the inverse Hessian of the action-value function. We provide a rigorous analysis of this sampling mechanism of three ME-DDP variants: Unimodal Gaussian ME-DDP, Multimodal Gaussian ME-DDP, and Stein Variational DDP. Furthermore, with navigation tasks of four robotic systems under cluttered environments, we conduct extensive benchmarking of three variants of the ME-DDP, against deterministic DDP, and one of the most successful sampling-based schemes, Model Predictive Path Integral (MPPI) control with three policy parameterizations and update laws that correspond to those of ME-DDPs. The results show that in low-dimensional systems where the cost landscapes are relatively simple and local information is sufficiently representative, our framework consistently outperforms MPPIs. In high-dimensional systems, MPPI can occasionally discover aggressive maneuvers that enable it to steer the systems faster than DDP-based methods, whereas our method maintains a higher, more stable success rate. Finally, we validate the practical efficacy of the framework through hardware experiments with a quadrotor navigating a dense, non-convex obstacle field, confirming the robustness of the proposed framework for real-world deployment.

Deep reinforcement learning (RL) offers a promising route to real-time power grid operation, yet large neural policies are costly to evaluate, hard to deploy on constrained hardware, and opaque to operators. We ask whether a Proximal Policy Optimization (PPO) agent for grid topology control can be compressed into compact tree-based surrogates without losing operational performance. A PPO teacher is trained on Grid2Op's standard 14-bus environment with a stability-oriented reward, using stress-focused data collection on critical, high-loading states. The policy is then distilled into a decision tree and a random forest. Across held-out validation episodes, both surrogates exceed the teacher in mean reward and survival length at a fraction of the inference cost. The decision tree shows high exact-action agreement with the PPO argmax and near-complete agreement within its top-ranked actions, while remaining small enough to be inspected directly. Feature-importance analysis reveals a representational shift: the PPO policy relies mainly on line-loading signals, while the distilled tree is driven primarily by bus-topology variables. These results suggest that stress-focused distillation can convert a black-box neural controller into a lightweight, auditable rule-like surrogate suited for real-time deployment, while also surfacing risks tied to deterministic actions and topology-specific generalization.

When a large language model under reinforcement learning commits a wrong reasoning step early in a trajectory, standard algorithms force it to keep generating until the maximum horizon, spending compute on tokens that never receive positive reward and polluting advantage estimates with post-failure noise. We propose ESPO (Early-Stopping Proximal Policy Optimization), which detects trajectory failure on-the-fly and terminates rollouts early. At each generation step, ESPO computes a surrogate regret using only the logits already computed during sampling, and terminates when the smoothed cumulative regret significantly exceeds its estimated values. Truncated trajectories are treated as absorbing failure states with a terminal reward, concentrating negative temporal-difference (TD) errors near the detected failure step without any additional reward model or human annotation. On DeepSeek-R1-Distill-Qwen-7B trained for mathematical reasoning, ESPO surpasses PPO on AIME2024 (46.28% vs. 45.25%), AMC2023 (85.83% vs. 82.94%), and MATH-500 (87.42% vs. 85.43%), while saving more than 20% rollout tokens cumulatively.

Proximal Policy Optimization (PPO) has become the de facto standard for training legged robots, thanks to its robustness and scalability in massively parallel simulation environments like IsaacLab. However, its on-policy nature makes it inherently sample-inefficient, preventing its use for continuous adaptation and fine-tuning on real hardware. Soft Actor-Critic (SAC), by contrast, is an off-policy algorithm that can reuse past experience, making it a natural candidate for sim-to-real transfer workflows where the same algorithm can be used both in simulation and for online learning on the real robot. Despite these advantages, SAC has consistently failed to match PPO's empirical performance in massively parallel training settings. This work identifies the root causes of this gap and introduces targeted modifications, covering policy initialization, timeout-aware critic targets, and multi-step return estimation, that enable SAC to train stably at scale. Evaluated across multiple legged robot platforms and diverse locomotion tasks, our approach closes the performance gap with PPO entirely.

Android malware detectors often degrade after deployment because of concept drift, while full retraining at each maintenance step is costly. We propose a chronological adaptive maintenance framework that models deployment-time maintenance as a sequential decision problem. The framework learns a stable latent representation through self-supervised learning during initialization, freezes the encoder, measures latent drift in the fixed representation space, and performs lightweight downstream adaptation using a trainable adapter and classification head. A proximal policy optimization controller selects low-cost maintenance actions based on the detector state, including current utility, retention on a fixed memory set, latent drift indicators, and update cost. We evaluate the framework under a causal deployment-style protocol on emulator and real Android malware datasets with static and dynamic features. Results show that the RL controller provides a strong cost-aware adaptation strategy, consistently remaining among the top-performing policies while achieving a favorable balance between temporal performance, memory retention, and maintenance cost under non-stationary deployment conditions.

The Flexible Job Shop Scheduling Problem (FJSP) is the optimal allocation of a set of jobs to machines. Two primary challenges persist in FJSP: the unpredictable arrival of future jobs and the combinatorial complexity of the problem, rendering it intractable for conventional mixed-integer linear programming solvers. This paper proposes an event-based \gls{DRL} approach to solve FJSP with random job arrivals. Specifically, we employ the Proximal Policy Optimization algorithm and use lightweight Multi-Layer Perceptrons to train the \gls{DRL} agent for minimizing the total completion time of all jobs. We design the state representation to be directly accessible from the environment, and limit the learning agent to selecting from among a set of well-established dispatching rules. Simulations show that our \gls{DRL} approach outperforms any of the individual dispatching rules on datasets with varying heterogeneity and job arrival rates. We benchmark our \gls{DRL} against an arrival-triggered mixed-integer linear programming solution and show that our method achieves good performance especially when the datasets are heterogeneous.

Skill atrophy, the gradual decline of human capability under AI assistance, poses a safety risk in shared-control of semi-autonomous systems, where operators may be unable to distinguish their own inputs from autonomous corrections. We propose Proximal State Nudging (PSN), a shared autonomy algorithm that jointly optimizes for skill development and task performance by nudging users toward states estimated to be most learnable. We first show that PSN outperforms existing shared autonomy baselines in balancing student improvement in unassisted reward with overall shared performance, using simulated students in the classic LunarLander environment. We then present, to the best of our knowledge, the first human subject studies of a planner incorporating learning-compatible shared autonomy: across two driving tasks in the CARLA simulator (High Performance Racing and Parallel Parking, n = 60), PSN produces up to 7x larger gains in unassisted skill than standard blended shared autonomy, while incurring 50% fewer collisions than unassisted self-practice.

Competitive multi-agent reinforcement learning in imperfect-information games requires agents to act under partial observability and against adversarial opponents, necessitating stochastic policies. While self-play reinforcement learning with Proximal Policy Optimization (PPO) has achieved strong empirical success, its standard advantage estimator, generalized advantage estimation, suffers from additional variance due to the sampling of stochastic future actions. This variance is amplified in equilibrium self-play because of the stochastic nature of the equilibrium policy and persists even when the critic is exact. We address this bottleneck by introducing $Q$-boosting, a variance-reduced advantage estimator based on a centralized action-value critic, and propose Variance-Reduced Policy Optimization (VRPO), incorporating this new estimator. The algorithm replaces sampled multi-step backups with a multi-step Expected SARSA$(λ)$ trace, computing policy expectations at each step to average out action-sampling noise, while retaining PPO's clipped objective and on-policy actor updates. Empirically, VRPO consistently achieves strong performance from mid-sized to large-scale games including Dou Dizhu and Heads-Up No-Limit Texas Hold'em.

This paper proposes a Shared Backbone Proximal Policy Optimization (Shared Backbone PPO) algorithm. By sharing the base module between the Actor and Critic networks, the algorithm achieves efficient training and improved performance. The algorithm is implemented in a connectivity-preserving multi-UAV swarm communication coverage task and compared with the standard PPO algorithm. Experimental results demonstrate that the proposed method achieves superior performance. Furthermore, a graph information aggregation module is incorporated into the model architecture to accommodate the communication conditions among agents. With the integration of this module, the algorithm remains effective, and the trained agent swarm exhibits a higher level of cooperation.

Contrastive reinforcement learning (CRL) learns goal-conditioned Q-values through a contrastive objective over state-action and goal representations, removing the need for hand-crafted reward functions. Despite impressive success in achieving viable self-supervised learning in RL, all existing CRL algorithms rely on off-policy optimisation and are mostly constrained to continuous action spaces, with little research invested in discrete environments. This leaves CRL disconnected from widely used and effective, modern on-policy training pipelines adopted across both single-agent and multi-agent RL in continuous and discrete environments. To establish a first connection, we introduce Contrastive Proximal Policy Optimisation (CPPO). CPPO is an on-policy contrastive RL algorithm that derives policy advantages directly from contrastive Q-values and optimises them via the standard PPO objective, without requiring a reward function or a replay buffer. We evaluate CPPO across continuous and discrete, single-agent and cooperative multi-agent tasks. Whilst the existence of an on-policy approach is inherently useful, we observe that \textbf{CPPO not only significantly outperforms the previous CRL baselines in 14 out of 18 tasks, but also matches or exceeds PPO's performance, which uses hand-crafted dense rewards, in 12 out of the 18 tasks tested.}

Multi-Agent Proximal Policy Optimization (MAPPO) is a variant of the Proximal Policy Optimization (PPO) algorithm, specifically tailored for multi-agent reinforcement learning (MARL). MAPPO optimizes cooperative multi-agent settings by employing a centralized critic with decentralized actors. However, in case of multi-dimensional environment, MAPPO can not extract optimal policy due to non-stationary agent observation. To overcome this problem, we introduce a novel approach, Entropy Regularization-based Proximal Policy Optimization (ERPPO). For the policy optimization, we first define the object detection ambiguity under multi-dimensional observation environment. Distributional Spatiotemporal Ambiguity (DSA) learner is trained to estimate object detection uncertainty in non-stationary constraints. Then, we enhance PPO with a novel Entropy Regularization term. This regularization dynamically adjusts the policy update by applying a stronger (L1) regularization in high-ambiguity observation to encourage significant exploratory actions and a weaker (L2) regularization in low-ambiguity observation to stabilize the proximal policy optimization. This approach is designed to enhance the probability of successful object localization in time-critical operations by reducing detection failures and optimizing search policy. Experiments on a testbed with AirSim-based maritime searching scenarios show that the proposed ERPPO improves accuracy performance. Our proposed method improves higher gradient than MAPPO. Qualitative results confirm that ERPPO effectiveness in terms of suppressing false detection in visually uncertain conditions.

Soft Actor-Critic (SAC) and its variants dominate Multi-Task Reinforcement Learning (MTRL) due to their off-policy sample efficiency, while on-policy methods such as Proximal Policy Optimization (PPO) remain underexplored. We diagnose that PPO in MTRL suffers from a previously overlooked issue: critic-side gradient ill-conditioning, which may cause tail tasks to stall while easy tasks dominate the value function's updates. To address this, we propose TOPPO (Tail-Optimized PPO), a reformulation of PPO via Critic Balancing -- a set of modules that improve gradient conditioning and balance learning dynamics across tasks. Unlike prior approaches that rely on modular architectures or large models, TOPPO targets the optimization bottleneck within PPO itself. Empirically, TOPPO achieves stronger mean and tail-task performance than published SAC-family and ARS-family baselines while using substantially fewer parameters and environment steps on Meta-World+ benchmark. Notably, TOPPO matches or surpasses strong SAC baselines early in training and maintains superior performance at full budget. Ablations confirm the effectiveness of each module in TOPPO and provide insights into their interactions. Our results demonstrate that, with proper optimization, on-policy methods can rival or exceed off-policy approaches in MTRL, challenging the prevailing reliance on SAC and highlighting critic-side gradient conditioning as the central bottleneck.

Decentralized multi-agent path finding (MAPF) routes a team of agents on a shared grid, each acting from its own local view. The standard solution trains one shared neural policy with Proximal Policy Optimization (PPO), a popular on-policy reinforcement learning algorithm. Such a policy works well on clean observations, but a small input perturbation on one agent often changes its action, which then blocks a neighbour, and the team jams. In this paper we present two training recipes that keep the same network and the same deployment loop, yet make the policy hold up under perturbed observations. The first recipe, Adv-PPO, trains the shared policy against worst-case perturbations of its own input and selects the checkpoint by performance under adversarial perturbation. The second recipe, Adv-PPO+MACER, fine-tunes that checkpoint with a small on-policy smoothness term whose gradient follows the certified radius of randomized smoothing. On POGEMA with 8x8 maps and four agents, the unprotected PPO policy reaches 95.8% clean success but only 2.5% under the strongest attack. Adv-PPO recovers worst-case success to 59.2% at one percentage point of clean cost. Adv-PPO+MACER recovers it to 77.5% +/- 6.0% across three independent seeds at less than one percentage point of clean cost. We support these numbers with per-attack curves, a certified action-stability sanity check (which measures the smoothed-policy wrapper, not the deployed argmax policy), and side-by-side rollout storyboards that show the failure mode and the fix inside one environment instance.

Stochastic trajectory optimization methods like STOMP enable planning with non-differentiable costs, offering substantial flexibility over gradient-based approaches. We show that STOMP implicitly minimizes the KL divergence from a Boltzmann trajectory distribution, revealing an elegant Variational Inference (VI) structure underlying its updates. Building on this insight, we propose the \textit{Proximal Inference for Stochastic Trajectory Optimization} (PISTO) algorithm that stabilizes the updates by augmenting the objective with a KL regularization between successive Gaussian proposals. This proximal formulation admits a trust-region interpretation and yields closed-form mean updates computable as expectations under a surrogate distribution. We estimate these expectations via importance-weighted Monte Carlo sampling, producing a simple, derivative-free algorithm that inherits STOMP's ability to handle non-differentiable and discontinuous costs without modification. On robot arm motion planning benchmarks, PISTO achieves an 89% success rate -- outperforming CHOMP (63%) and STOMP (68%) -- while producing shorter, smoother paths at twice the speed of competing stochastic methods. We further validate PISTO on contact-rich MuJoCo locomotion and manipulation tasks, where it consistently outperforms both CEM and MPPI baselines in reward.

Reinforcement learning with verifiable rewards (RLVR), due to the deterministic verification, becomes a dominant paradigm for enhancing the reasoning ability of large language models (LLMs). The community witnesses the rapid change from the Proximal Policy Optimization (PPO) to Group Relative Policy Optimization (GRPO), in which GRPO reduces the complicated advantage estimation with simple estimation over grouped positive and negative rollouts. However, we note that negative rollouts may admit no gradation of failure severity, and the combinatorial vastness makes penalizing a few sampled negatives unlikely to cover a meaningful reward signal under sparse binary rewards. In this work, we propose Positive-Only Policy Optimization (POPO), a novel RLVR framework in which learning can occur exclusively via online positive rollouts. Specifically, POPO utilizes bounded importance sampling over the positive rollout set. Thus, no disjoint negative rollouts are used for the gradient guidance. We show that implicit negative gradients can emerge naturally through reinforcing the positive probability via rollouts redistribution. Next, POPO stabilizes the policy optimization through two mechanisms. First, it applies a siamese policy network with a momentum-based adaptation law for stabilized policy evolution. Second, we replace the KL-divergence with a bounded similarity penalty term in the siamese representation space. We conduct extensive experiments using publicly available, well-established text-LLM models, e.g., the Qwen family, across all-level mathematical benchmarks. Our experiment demonstrates that POPO achieves performance comparable to, or even superior to GRPO. Notably, we show that POPO can achieve 36.67% in AIME 2025 with Qwen-Math-7B, outperforming GRPO 30.00%. Our ablation and sweep studies further illustrate the necessity and robustness of POPO components.

Proximal Policy Optimization (PPO) dominates reinforcement learning and LLM alignment, yet its hard-clipping mechanism and unconstrained alternatives (e.g., SPO) sit at two extremes of a stability-efficiency dilemma. We argue that this dilemma is best understood dynamically: a surrogate objective is a feedback law on the probability ratio, and its clipping/penalty shape defines a gain field that drives the update dynamics. PPO's clip induces a dead zone (zero feedback outside the trust region), leaving the policy to drift open-loop under momentum; SPO's quadratic penalty induces an unbounded, linearly growing gain that stiffens the dynamics and destabilizes under aggressive step sizes. Guided by this view, we derive Anchored Neighborhood Optimization (ANO), which designs the gain field directly: a $C^\infty$ shaping kernel that anchors the identity map at $r{=}1$, peaks exactly at a prescribed trust-region boundary $1{+}ε$, bounds the push on severely off-policy samples by a tunable $κ_{+}$, and exerts a bounded, redescending pull of tunable depth $κ_{-}$ on extreme outliers. The three hyperparameters have decoupled roles, and all internal constants are solved in closed form. Empirically, ANO ranks first on both Atari (40 games) and MuJoCo in IQM and Median of normalized scores. While the runner-up differs across domains (PAPO on Atari, SPO on MuJoCo), ANO is the only method consistently at the top. Under a learning-rate stress test ($3\times10^{-4}\!\to\!10^{-3}$), ANO degrades by only $0.9\%$ whereas PPO collapses by $54.5\%$, and the stressed ANO still outperforms PPO and PAPO at their best-tuned learning rates.

Developing effective test cases capable of thoroughly exercising large-scale software systems is inherently difficult, especially if such systems have voluminous, complex, and deeply nested source codes. In this work, we present a novel approach for generating test cases using a reinforcement learning-driven agentic framework where Proximal Policy Optimization (PPO) is coupled with an LLM engine to guide prompt selection during test generation. Our approach consists of two phases. In Phase I, the ToT-guided optimization agent partitions and minimizes the source code by removing redundancies without changing the functional behavior of the source code. In Phase II, a PPO-based policy network is trained to solve the problem of selecting prompts among eight different prompting techniques, such as Boundary Value Analysis, Random Fuzzing, etc., based on the inputted 11-dimensional state vector representing the source code complexity metrics and live coverage metrics to direct the LLM engine towards exploring unvisited paths in the program. The PPO agent receives rewards based on a combination of increases in line and branch coverages, penalties for unexplored branches, and rewards for reducing source code length. From experiments conducted on twenty benchmark programs, it is evident that the proposed approach, PPO-LLM, outperforms CBMC, kS-LLM, and kS-LLM++ in terms of branch and line coverage in almost all cases, for various loop bound values ranging from BOUND1 to BOUND2000. While at BOUND~1, the coverage of branches is 100% using PPO-LLM on the PALS suite, in comparison, it is around 86.8% using kS-LLM++. This confirms that adaptive prompt selection driven by PPO substantially outperforms static prompting strategies on PALS type programs.

Deep Reinforcement Learning (DRL) algorithms often require a large amount of data and struggle in sparse-reward domains with long planning horizons and multiple sub-goals. In this paper, we propose a neuro-symbolic extension of Proximal Policy Optimization (PPO) that transfers partial logical policy specifications learned in easier instances to guide learning in more challenging settings. We introduce two integrations of symbolic guidance: (i) H-PPO-Product, which biases the action distribution at sampling time, and (ii) H-PPO-SymLoss, which augments the PPO loss with a symbolic regularization term. We evaluate our methods on three benchmarks (OfficeWorld, WaterWorld, and DoorKey), showing consistently faster learning and higher return at convergence than PPO and a Reward Machine baseline, also under imperfect symbolic knowledge.

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

Autonomous bicycles offer a promising agile solution for urban mobility and last-mile logistics. However, conventional control strategies often struggle with underactuated nonlinear dynamics, suffering from sensitivity to model mismatches and limited adaptability to real-world uncertainties. To address this, we develop CycleRL, a comprehensive sim-to-real framework for robust autonomous bicycle control. Our approach establishes a direct perception-to-action mapping within the high-fidelity NVIDIA Isaac Sim environment, leveraging Proximal Policy Optimization (PPO) to optimize the control policy. The framework features a composite reward function tailored for concurrent balance maintenance, velocity tracking, and steering control. Crucially, systematic domain randomization is employed to reduce the reliance on precise system modeling, bridge the simulation-to-reality gap and facilitate direct transfer. In simulation, CycleRL achieves promising performance, including a 99.90% balance success rate, a heading tracking error of 1.15°, and a velocity tracking error of 0.18 m/s. These quantitative results, coupled with successful hardware deployment, validate DRL as an effective paradigm for autonomous bicycle control, offering superior adaptability over traditional methods. Video demonstrations are available at https://cpnt-lab.github.io/CycleRL/.

Off-road autonomous driving poses significant challenges such as navigating unmapped, variable terrain with uncertain and diverse dynamics. Addressing these challenges requires effective long-horizon planning and adaptable control. Reinforcement Learning (RL) offers a promising solution by learning control policies directly from interaction. However, because off-road driving is a long-horizon task with low-signal rewards, standard RL methods are challenging to apply in this setting. We introduce TADPO, a novel policy gradient formulation that extends Proximal Policy Optimization (PPO), leveraging off-policy trajectories for teacher guidance and on-policy trajectories for student exploration. Building on this, we develop a vision-based, end-to-end RL system for high-speed off-road driving, capable of navigating extreme slopes and obstacle-rich terrain. We demonstrate our performance in simulation and, importantly, zero-shot sim-to-real transfer on a full-scale off-road vehicle. To our knowledge, this work represents the first deployment of RL-based policies on a full-scale off-road platform.

Penetration testing, the simulation of cyberattacks to identify security vulnerabilities, presents a sequential decision-making problem well-suited for reinforcement learning (RL) automation. Like many applications of RL to real-world problems, partial observability presents a major challenge, as it invalidates the Markov property present in Markov Decision Processes (MDPs). Partially Observable MDPs require history aggregation or belief state estimation to learn successful policies. We investigate stochastic, partially observable penetration testing scenarios over host networks of varying size, aiming to better reflect real-world complexity through more challenging and representative benchmarks. This approach leads to the development of more robust and transferable policies, which are crucial for ensuring reliable performance across diverse and unpredictable real-world environments. Using vanilla Proximal Policy Optimization (PPO) as a baseline, we compare a selection of PPO-based variants designed to mitigate partial observability, including frame-stacking, augmenting observations with historical information, and employing LSTM or TrXL architectures. We conduct a systematic empirical analysis of these algorithms across different host network sizes. We find that this task greatly benefits from history aggregation. Converging up to four times faster than other approaches. Manual inspection of the learned policies by the algorithms reveals clear distinctions and provides insights that go beyond quantitative results.

Proficient game agents with diverse play styles enrich the gaming experience and enhance the replay value of games. However, recent advancements in game AI based on reinforcement learning have predominantly focused on improving proficiency, whereas methods based on evolution algorithms generate agents with diverse play styles but exhibit subpar performance compared to RL methods. To address this gap, this paper proposes Mixed Proximal Policy Optimization (MPPO), a method designed to improve the proficiency of existing suboptimal agents while retaining their distinct styles. MPPO unifies loss objectives for both online and offline samples and introduces an implicit constraint to approximate demonstrator policies by adjusting the empirical distribution of samples. Empirical results across environments of varying scales demonstrate that MPPO achieves proficiency levels comparable to, or even superior to, pure online algorithms while preserving demonstrators' play styles. This work presents an effective approach for generating highly proficient and diverse game agents, ultimately contributing to more engaging gameplay experiences.

Model-free and reinforcement learning-based adaptive filtering methods are gaining traction for denoising in dynamic, non-stationary environments such as wireless signal channels, biomedical monitoring, and sensor networks. Traditional filters such as LMS, RLS, Wiener, and Kalman are often limited by assumptions of stationarity, the need for exact noise statistics, or fragile parameter tuning. This paper proposes an adaptive filtering framework using Proximal Policy Optimization (PPO), guided by a composite reward that balances SNR improvement, MSE reduction, and residual smoothness. We frame adaptive filtering as a Markov decision process and train a PPO agent to adjust filter coefficients directly in response to changing noise. Experiments on synthetic nonstationary signals with diverse noise types show that the PPO agent generalizes beyond its training distribution. Moreover, real-world analysis is made and evaluated on ECG recordings from the MIT-BIH Noise Stress Test Database corrupted by baseline wander, electrode motion, and muscle artifacts. The learned PPO policy achieves real-time inference and slightly outperforms strong classical baselines on ECG denoising. These results demonstrate the viability of policy-gradient reinforcement learning as a computationally efficient and flexible tool for adaptive filtering in nonlinear, time-varying dynamical systems.

Proximal Policy Optimization (PPO) is a popular model-free reinforcement learning algorithm, esteemed for its simplicity and efficacy. However, due to its inherent on-policy nature, its proficiency in harnessing data from disparate policies is constrained. This paper introduces a novel off-policy extension to the original PPO method, christened Transductive Off-policy PPO (ToPPO). Herein, we provide theoretical justification for incorporating off-policy data in PPO training and prudent guidelines for its safe application. Our contribution includes a novel formulation of the policy improvement lower bound for prospective policies derived from off-policy data, accompanied by a computationally efficient mechanism to optimize this bound, underpinned by assurances of monotonic improvement. Comprehensive experimental results across six representative tasks underscore ToPPO's promising performance.

Uncertainties in transition dynamics pose a critical challenge in reinforcement learning (RL), often resulting in performance degradation of trained policies when deployed on hardware. Many robust RL approaches follow two strategies: enforcing smoothness in actor or actor-critic modules with Lipschitz regularization, or learning robust Bellman operators. However, the first strategy does not investigate the impact of critic-only Lipschitz regularization on policy robustness, while the second lacks comprehensive validation in real-world scenarios. Building on this gap and prior work, we propose PPO-PGDLC, an algorithm based on Proximal Policy Optimization (PPO) that integrates Projected Gradient Descent (PGD) with a Lipschitz-regularized critic (LC). The PGD component calculates the adversarial state within an uncertainty set to approximate the robust Bellman operator, and the Lipschitz-regularized critic further improves the smoothness of learned policies. Experimental results on two classic control tasks and one real-world robotic locomotion task demonstrate that, compared to several baseline algorithms, PPO-PGDLC achieves better performance and predicts smoother actions under environmental perturbations.

Identifying the most suitable variables to represent the state is a fundamental challenge in Reinforcement Learning (RL). These variables must efficiently capture the information necessary for making optimal decisions. In order to address this problem, in this paper, we introduce the Transfer Entropy Redundancy Criterion (TERC), an information-theoretic criterion, which determines if there is entropy transferred from observable state variables to actions during training. We define an algorithm based on TERC that provably excludes variables from the observable state that do not affect the agent's policy during learning. This yields compact state representations that reduce inference time by up to 2.6 times. Our approach is policy-dependent, making it agnostic to the underlying learning algorithm. The efficiency gains we demonstrate arise at retraining and inference time on the reduced state. Our method improves both retraining and inference efficiency. We demonstrate its effectiveness across three distinct algorithm classes, namely tabular Q-learning, Actor-Critic, and Proximal Policy Optimization (PPO), evaluated in a range of environments. Furthermore, to highlight the differences between the proposed methodology and the current state-of-the-art feature selection approaches, we present a series of controlled experiments on synthetic data, before generalizing to real-world decision-making tasks. We also introduce a representation of the problem that compactly captures the transfer of information from observable state variables to actions as Bayesian networks.