Proximal Policy Optimization

We present Territory Paint Wars, a minimal competitive multi-agent reinforcement learning environment implemented in Unity, and use it to systematically investigate failure modes of Proximal Policy Optimisation (PPO) under self-play. A first agent trained for $84{,}000$ episodes achieves only $26.8\%$ win rate against a uniformly-random opponent in a symmetric zero-sum game. Through controlled ablations we identify five implementation-level failure modes -- reward-scale imbalance, missing terminal signal, ineffective long-horizon credit assignment, unnormalised observations, and incorrect win detection -- each of which contributes critically to this failure in this setting. After correcting these issues, we uncover a distinct emergent pathology: competitive overfitting, where co-adapting agents maintain stable self-play performance while generalisation win rate collapses from $73.5\%$ to $21.6\%$. Critically, this failure is undetectable via standard self-play metrics: both agents co-adapt equally, so the self-play win rate remains near $50\%$ throughout the collapse. We propose a minimal intervention -- opponent mixing, where $20\%$ of training episodes substitute a fixed uniformly-random policy for the co-adaptive opponent -- which mitigates competitive overfitting and restores generalisation to $77.1\%$ ($\pm 12.6\%$, $10$ seeds) without population-based training or additional infrastructure. We open-source Territory Paint Wars to provide a reproducible benchmark for studying competitive MARL failure modes.

Traditional RL algorithms like Proximal Policy Optimization (PPO) typically train on the entire rollout buffer, operating under the assumption that all generated episodes provide a beneficial optimization signal. However, these episodes frequently contain noisy or unfaithful reasoning, which can degrade model performance and slow down training. In this paper, we propose Influence-Guided PPO (I-PPO), a novel framework that integrates data attribution into the RL post-training loop. By calculating an influence score for each episode using a gradient-based approximation, I-PPO identifies and eliminates episodes that are anti-aligned with a validation gradient. Our experiments demonstrate that I-PPO consistently outperforms SFT and PPO baselines. We show that our filtering process acts as an intrinsic early stopping mechanism, accelerating training efficiency while effectively reducing unfaithful CoT reasoning.

Reinforcement learning has become a central post-training paradigm for improving LLM and agent capabilities. Yet existing RL post-training methods share a common blind spot: they construct local learning signals from sampled trajectories, rewards, or feedback-conditioned targets, then update the policy without explicitly verifying whether the resulting policy outperforms its predecessor. Optimizing these local signals does not necessarily produce a better policy, while finite sampling, generation stochasticity and feedback noise can further widen this gap. We argue that the missing ingredient is policy improvement feedback: the ability to measure progress across policy iterations. We introduce Policy Improvement Reinforcement Learning (PIRL), which formulates inter-iteration performance gain as an explicit objective structurally aligned with final task performance. Building on PIRL, we propose Policy Improvement Policy Optimization (PIPO), a plug-in closed-loop framework that verifies the previous update against a sliding-window historical performance anchor. PIPO uses this improvement feedback to modulate the local learning signal of the base policy optimization algorithm, reinforcing updates associated with measured progress and suppressing those associated with performance drops. We provide theoretical evidence that PIPO locally aligns policy updates with the PIRL improvement objective. Experiments on mathematical reasoning, code, tool-use, and self-distillation settings show that PIPO yields consistent gains across PPO, group-relative, and self-distillation policy optimization families.

Reinforcement Learning (RL) agents often struggle with inefficient exploration, particularly in environments with sparse rewards. Traditional exploration strategies can lead to slow learning and suboptimal performance because agents fail to systematically build on previously successful experiences, thereby reducing sample efficiency. To tackle this issue, we propose a self-imitating on-policy algorithm that enhances exploration and sample efficiency by leveraging past high-reward state-action pairs to guide policy updates. Our method incorporates self-imitation by using optimal transport distance in dense reward environments to prioritize state visitation distributions that match the most rewarding trajectory. In sparse-reward environments, we uniformly replay successful self-encountered trajectories to facilitate structured exploration. Experimental results across diverse environments demonstrate substantial improvements in learning efficiency, including MuJoCo for dense rewards and the partially observable 3D Animal-AI Olympics and multi-goal PointMaze for sparse rewards. Our approach achieves faster convergence and significantly higher success rates compared to state-of-the-art self-imitating RL baselines. These findings underscore the potential of self-imitation as a robust strategy for enhancing exploration in RL, with applicability to more complex tasks.

The efficiency of game engines and policy optimization algorithms is crucial for training reinforcement learning (RL) agents in complex sequential decision-making tasks, such as Tetris. Existing Tetris implementations suffer from low simulation speeds, suboptimal state evaluation, and inefficient training paradigms, limiting their utility for large-scale RL research. To address these limitations, this paper proposes a high-performance Tetris AI framework based on bitboard optimization and improved RL algorithms. First, we redesign the Tetris game board and tetrominoes using bitboard representations, leveraging bitwise operations to accelerate core processes (e.g., collision detection, line clearing, and Dellacherie-Thiery Features extraction) and achieve a 53-fold speedup compared to OpenAI Gym-Tetris. Second, we introduce an afterstate-evaluating actor network that simplifies state value estimation by leveraging Tetris afterstate property, outperforming traditional action-value networks with fewer parameters. Third, we propose a buffer-optimized Proximal Policy Optimization (PPO) algorithm that balances sampling and update efficiency, achieving an average score of 3,829 on 10x10 grids within 3 minutes. Additionally, we develop a Python-Java interface compliant with the OpenAI Gym standard, enabling seamless integration with modern RL frameworks. Experimental results demonstrate that our framework enhances Tetris's utility as an RL benchmark by bridging low-level bitboard optimizations with high-level AI strategies, providing a sample-efficient and computationally lightweight solution for scalable sequential decision-making research.

Legged locomotion in unstructured environments demands not only high-performance control policies but also formal guarantees to ensure robustness under perturbations. Control methods often require carefully designed reference trajectories, which are challenging to construct in high-dimensional, contact-rich systems such as quadruped robots. In contrast, Reinforcement Learning (RL) directly learns policies that implicitly generate motion, and uniquely benefits from access to privileged information, such as full state and dynamics during training, that is not available at deployment. We present ContractionPPO, a framework for certified robust planning and control of legged robots by augmenting Proximal Policy Optimization (PPO) RL with a state-dependent contraction metric layer. This approach enables the policy to maximize performance while simultaneously producing a contraction metric that certifies incremental exponential stability of the simulated closed-loop system. The metric is parameterized as a Lipschitz neural network and trained jointly with the policy, either in parallel or as an auxiliary head of the PPO backbone. While the contraction metric is not deployed during real-world execution, we derive upper bounds on the worst-case contraction rate and show that these bounds ensure the learned contraction metric generalizes from simulation to real-world deployment. Our hardware experiments on quadruped locomotion demonstrate that ContractionPPO enables robust, certifiably stable control even under strong external perturbations.

Urban Vehicular Ad-Hoc Networks (VANETs) can become fragmented because buildings obstruct wireless links and vehicle mobility continuously changes the network topology. Unmanned Aerial Vehicles (UAVs) can serve as mobile relays, but Deep Reinforcement Learning (DRL)-based deployment often suffers from inefficient exploration because it lacks road-topology guidance. To address this problem, we propose Semantic-Augmented DRL (SA-DRL), which models network fragmentation over the road topology and aligns a pretrained Large Language Model (LLM) to generate a topology-dependent action prior from dynamic traffic states. The resulting Semantic-Augmented PPO (SA-PPO) algorithm combines this prior with the PPO policy through Logit Fusion, guiding exploration toward promising intersections while retaining adaptation through environmental returns. Simulations driven by real-world urban trajectories show that SA-PPO reaches the final converged reward of Vanilla PPO using only 28.6% of its training episodes. It improves the average number of vehicles in connected components and the average connected-component size by 7.9% and 8.7%, respectively, while reducing UAV energy consumption by 21.3%.

The integration of satellite communication networks with next-generation (NG) technologies is a promising approach towards global connectivity. However, the quality of services is highly dependant on the availability of accurate channel state information (CSI). Channel estimation in satellite communications is challenging due to the high propagation delay between terrestrial users and satellites, which results in outdated CSI observations on the satellite side. In this paper, we study the downlink transmission of multiple satellites acting as distributed base stations (BS) to mobile terrestrial users. We propose a multi-agent reinforcement learning (MARL) algorithm which aims for maximising the sum-rate of the users, while coping with the outdated CSI. We design a novel bi-level optimisation, procedure themes as dual stage proximal policy optimisation (DS-PPO), for tackling the problem of large continuous action spaces as well as of independent and non-identically distributed (non-IID) environments in MARL. Specifically, the first stage of DS-PPO maximises the sum-rate for an individual satellite and the second stage maximises the sum-rate when all the satellites cooperate to form a distributed multi-antenna BS. Our numerical results demonstrate the robustness of DS-PPO to CSI imperfections as well as the sum-rate improvement attached by the use of DS-PPO. In addition, we provide the convergence analysis for the DS-PPO along with the computational complexity.

Morphology-control co-design concerns the coupled optimization of an agent's body structure and control policy. This problem exhibits a bi-level structure, where the control dynamically adapts to the morphology to maximize performance. Existing methods typically neglect the control's adaptation dynamics by adopting a single-level formulation that treats the control policy as fixed when optimizing morphology. This can lead to inefficient optimization, as morphology updates may be misaligned with control adaptation. In this paper, we revisit the co-design problem from a game-theoretic perspective, modeling the intrinsic coupling between morphology and control as a novel variant of a Stackelberg game. We propose Stackelberg Proximal Policy Optimization (Stackelberg PPO), which explicitly incorporates the control's adaptation dynamics into morphology optimization. By modeling this intrinsic coupling, our method aligns morphology updates with control adaptation, thereby stabilizing training and improving learning efficiency. Experiments across diverse co-design tasks demonstrate that Stackelberg PPO outperforms standard PPO in both stability and final performance, opening the way for dramatically more efficient robotics designs.

Proximal policy optimization (PPO) approximates the trust region update using multiple epochs of clipped SGD. Each epoch may drift further from the natural gradient direction, creating path-dependent noise. To understand this drift, we can use Fisher information geometry to decompose policy updates into signal (the natural gradient projection) and waste (the Fisher-orthogonal residual that consumes trust region budget without first-order surrogate improvement). Empirically, signal saturates but waste grows with additional epochs, creating an optimization-depth dilemma. We propose Consensus Aggregation for Policy Optimization (CAPO), which redirects compute from depth to width: $K$ PPO replicates are optimized on the same batch, differing only in minibatch shuffling order, and then aggregated into a consensus. We study aggregation in two spaces: Euclidean parameter space, and the natural parameter space of the policy distribution via the logarithmic opinion pool. In natural parameter space, the consensus provably achieves higher KL-penalized surrogate and tighter trust region compliance than the mean expert; parameter averaging inherits these guarantees approximately. On continuous control tasks, CAPO outperforms PPO and compute-matched deeper baselines under fixed sample budgets by up to 8.6x. CAPO demonstrates that policy optimization can be improved by optimizing wider, rather than deeper, without additional environment interactions.

Unmanned aerial vehicles (UAVs) are increasingly used to support time-critical medical supply delivery, providing rapid and flexible logistics during emergencies and resource shortages. However, effective deployment of UAV fleets requires coordination mechanisms capable of prioritizing medical requests, allocating limited aerial resources, and adapting delivery schedules under uncertain operational conditions. This paper presents a multi-agent reinforcement learning (MARL) framework for coordinating UAV fleets in stochastic medical delivery scenarios where requests vary in urgency, location, and delivery deadlines. The problem is formulated as a partially observable Markov decision process (POMDP) in which UAV agents maintain awareness of medical delivery demands while having limited visibility of other agents due to communication and localization constraints. The proposed framework employs Proximal Policy Optimization (PPO) as the primary learning algorithm and evaluates several variants, including asynchronous extensions, classical actor--critic methods, and architectural modifications to analyze scalability and performance trade-offs. The model is evaluated using real-world geographic data from selected clinics and hospitals extracted from the OpenStreetMap dataset. The framework provides a decision-support layer that prioritizes medical tasks, reallocates UAV resources in real time, and assists healthcare personnel in managing urgent logistics. Experimental results show that classical PPO achieves superior coordination performance compared to asynchronous and sequential learning strategies, highlighting the potential of reinforcement learning for adaptive and scalable UAV-assisted healthcare logistics.

Deep Reinforcement Learning systems are highly sensitive to the learning rate (LR), and selecting stable and performant training runs often requires extensive hyperparameter search. In Proximal Policy Optimization (PPO) actor--critic methods, small LR values lead to slow convergence, whereas large LR values may induce instability or collapse. We analyse this phenomenon from the behavior of the hidden neurons in the network using the Overfitting-Underfitting Indicator (OUI), a metric that quantifies the balance of binary activation patterns over a fixed probe batch. We introduce an efficient batch-based formulation of OUI and derive a theoretical connection between LR and activation sign changes, clarifying how a correct evolution of the neuron's inner structure depends on the step size. Empirically, across three discrete-control environments and multiple seeds, we show that OUI measured at only 10% of training already discriminates between LR regimes. We observe a consistent asymmetry: critic networks achieving highest return operate in an intermediate OUI band (avoiding saturation), whereas actor networks achieving highest return exhibit comparatively high OUI values. We then compare OUI-based screening rules against early return, clip-based, divergence-based, and flip-based criteria under matched recall over successful runs. In this setting, OUI provides the strongest early screening signal: OUI alone achieves the best precision at broader recall, while combining early return with OUI yields the highest precision in best-performing screening regimes, enabling aggressive pruning of unpromising runs without requiring full training.

Patient no-shows disrupt outpatient clinic operations, reduce productivity, and may delay necessary care. Clinics often adopt overbooking or double-booking to mitigate these effects. However, poorly calibrated policies can increase congestion and waiting times. Most existing methods rely on fixed heuristics and fail to adapt to real-time scheduling conditions or patient-specific no-show risk. To address these limitations, we propose an adaptive outpatient double-booking framework that integrates individualized no-show prediction with multi-objective reinforcement learning. The scheduling problem is formulated as a Markov decision process, and patient-level no-show probabilities estimated by a Multi-Head Attention Soft Random Forest model are incorporated in the reinforcement learning state. We develop a Multi-Policy Proximal Policy Optimization method equipped with a Multi-Policy Co-Evolution Mechanism. Under this mechanism, we propose a novel τ rule based on Kullback-Leibler divergence that enables selective knowledge transfer among behaviorally similar policies, improving convergence and expanding the diversity of trade-offs. In addition, SHapley Additive exPlanations is used to interpret both the predicted no-show risk and the agent's scheduling decisions. The proposed framework determines when to single-book, double-book, or reject appointment requests, providing a dynamic and data-driven alternative to conventional outpatient scheduling policies.

On-policy agents discard trajectories after each update, including rare high-return episodes. We propose Optimistic Policy Regularization (OPR), which turns those episodes into a closed-form reward bonus: we estimate an elite action prior from top-quartile episodes and add a \reviewblue{bounded transform of the log-ratio} of the prior to the policy's action distribution. OPR needs no auxiliary network, value gate, off-policy correction, or adversarial loop. It is a one-line modification of Proximal Policy Optimization (PPO)'s reward; yet, on 49 Atari games at 10M steps, $5\times$ fewer agent decisions than the 200M-frame baselines, it reaches a 148.4% median human-normalized score (HNS; 196.9% interquartile mean): higher scores than published PPO on $36/49$ games ($p{=}0.0014$) and a higher aggregate median than self-imitation learning, which falls well below OPR when frames and backbone are matched. We pair the method with a theory of when it works. The underlying log-ratio has an exact forward-KL interpretation; its pre-advantage placement propagates the signal through Generalized Advantage Estimation; and, under an idealized local update, its first-order effect depends on a prior-advantage alignment whose sign indicates help or harm. Since alignment varies across tasks and runs, we also study an online gating extension. On a ten-game set, it outperforms the backbone by $+17.4$ median HNS on average across seeds. Controlled experiments test temporal propagation and the tradeoffs of state conditioning and gating, supporting OPR as a simple regularizer with an analysis of where to shape.

An agent's performance stagnating at a suboptimal level is a common problem in deep on-policy RL. Focusing on PPO, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimisation challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. Looking deeper, PPO alternates between sampling rollouts from several parallel environments online using the current policy (which we call the "outer loop") and performing repeated minibatch SGD steps against this offline dataset (the "inner loop"). In our work, we abstract away the inner loop, and conceptually model the outer loop as standard stochastic optimisation. The step size is then controlled by the regularisation strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This framing predicts that, much like in SGD, if the outer step size is too large relative to the noise, updates become uninformative and lead to the policy thrashing around a local optimum instead of converging. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We validate the predictions of our model and conclude that increasing the number of parallel environments is a simple way to avoid these plateaus by simultaneously altering both these factors. Applying our analysis and scaling PPO to more than 1M parallel environments enables monotonic performance improvement up to one trillion transitions and leads to vastly superior performance compared to prior baselines in a complex open-ended domain.

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.

Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck: fixed bounds strictly constrain the upward update margin of low-probability actions, disproportionately suppressing high-advantage tail strategies and inducing rapid entropy collapse. To address this, we introduce Band-constrained Policy Optimization (BandPO). BandPO replaces canonical clipping with Band, a unified theoretical operator that projects trust regions defined by f-divergences into dynamic, probability-aware clipping intervals. Theoretical analysis confirms that Band effectively resolves this exploration bottleneck. We formulate this mapping as a convex optimization problem, guaranteeing a globally optimal numerical solution while deriving closed-form solutions for specific divergences. Extensive experiments across diverse models and datasets demonstrate that BandPO consistently outperforms canonical clipping and Clip-Higher, while robustly mitigating entropy collapse.

Reinforcement learning (RL) has been extensively employed in a wide range of decision-making problems, such as games and robotics. Recently, diffusion policies have shown strong potential in modeling multi-modal behaviors, enabling more diverse and flexible action generation compared to the conventional Gaussian policy. Despite various attempts to combine RL with diffusion, a key challenge is the difficulty of computing action log-likelihood under the diffusion model. This greatly hinders the direct application of diffusion policies in on-policy reinforcement learning. Most existing methods calculate or approximate the log-likelihood through the entire denoising process in the diffusion model, which can be memory- and computationally inefficient. To overcome this challenge, we propose a novel and efficient method to train a diffusion policy in an on-policy setting that requires only evaluating a simple Gaussian probability. This is achieved by aligning the policy iteration with the diffusion process, which is a distinct paradigm compared to previous work. Moreover, our formulation can naturally handle entropy regularization, which is often difficult to incorporate into diffusion policies. Experiments demonstrate that the proposed method produces multimodal policy behaviors and achieves superior performance on a variety of benchmark tasks in both IsaacLab and MuJoCo Playground.

Real-world reinforcement learning systems must operate under distributional drift in their observation streams, yet most policy architectures implicitly assume fully observed and noise-free states. We study robustness of Proximal Policy Optimization (PPO) under temporally persistent sensor failures that induce partial observability and representation shift. To respond to this drift, we augment PPO with temporal sequence models, including Transformers and State Space Models (SSMs), to enable policies to infer missing information from history and maintain performance. Under a stochastic sensor failure process, we prove a high-probability bound on infinite-horizon reward degradation that quantifies how robustness depends on policy smoothness and failure persistence. Empirically, on MuJoCo continuous-control benchmarks with severe sensor dropout, we show Transformer-based sequence policies substantially outperform MLP, RNN, and SSM baselines in robustness, maintaining high returns even when large fractions of sensors are unavailable. These results demonstrate that temporal sequence reasoning provides a principled and practical mechanism for reliable operation under observation drift caused by sensor unreliability.

Bio-inspired aquatic propulsion offers high thrust and maneuverability but is prone to destabilizing forces such as lift fluctuations, which are further amplified by six-degree-of-freedom (6-DoF) fluid coupling. We formulate quadrupedal swimming as a constrained optimization problem that maximizes forward thrust while minimizing destabilizing fluctuations. Our proposed framework, Accelerated Constrained Proximal Policy Optimization with a PID-regulated Lagrange multiplier (ACPPO-PID), enforces constraints with a PID-regulated Lagrange multiplier, accelerates learning via conditional asymmetric clipping, and stabilizes updates through cycle-wise geometric aggregation. Initialized with imitation learning and refined through on-hardware towing-tank experiments, ACPPO-PID produces control policies that transfer effectively to quadrupedal free-swimming trials. Results demonstrate improved thrust efficiency, reduced destabilizing forces, and faster convergence compared with state-of-the-art baselines, underscoring the importance of constraint-aware safe RL for robust and generalizable bio-inspired locomotion in complex fluid environments.

This paper proposes Proximal Policy Optimization with Linear Temporal Logic Constraints (PPO-LTL), a framework that integrates safety constraints written in LTL into PPO for safe reinforcement learning. LTL constraints offer rigorous representations of complex safety requirements, such as regulations that broadly exist in robotics, enabling systematic monitoring of safety requirements. Violations against LTL constraints are monitored by limit-deterministic Büchi automata, and then translated by a logic-to-cost mechanism into penalty signals. The signals are further employed for guiding the policy optimization via the Lagrangian scheme. Extensive experiments on the Zones and CARLA environments show that our PPO-LTL can consistently reduce safety violations, while maintaining competitive performance, against the state-of-the-art methods. The code is at https://github.com/EVIEHub/PPO-LTL.

While reinforcement learning (RL) has been central to the recent success of large language models (LLMs), RL optimization is notoriously unstable, especially when compared to supervised fine-tuning (SFT). In this work, we investigate the stability gap between SFT and RL from a gradient-based perspective, and show that the convexity of the SFT loss with respect to model logits plays a key role in enabling stable training. Our theoretical analysis demonstrates that this property induces favorable gradient directionality during optimization. In contrast, Proximal Policy Optimization (PPO), a widely adopted policy gradient algorithm utilizing a clipped surrogate objective, lacks this stabilizing property. Motivated by this observation, we propose Logits Convex Optimization (LCO), a simple yet effective policy optimization framework that aligns the learned policy with an optimal target derived from the original RL objective, thereby emulating the stabilizing effects of logits-level convexity. Extensive experiments across multiple model families show that our LCO framework consistently improves training stability and outperforms conventional RL methods on a broad range of benchmarks.

Reinforcement learning (RL) actor-critic algorithms enable autonomous learning but often require a large number of environment interactions, which limits their applicability in robotics. Leveraging expert data can reduce the number of required environment interactions. A common approach is actor pretraining, where the actor network is initialized via behavioral cloning on expert demonstrations and subsequently fine-tuned with RL. In contrast, the initialization of the critic network has received little attention, despite its central role in policy optimization. This paper proposes a pretraining approach for actor-critic algorithms like Proximal Policy Optimization (PPO) that uses expert demonstrations to initialize both networks. The actor is pretrained via behavioral cloning, while the critic is pretrained using returns obtained from rollouts of the pretrained policy. The approach is evaluated on 15 simulated robotic manipulation and locomotion tasks. Experimental results show that actor-critic pretraining improves sample efficiency by 86.1% on average compared to no pretraining and by 30.9% to actor-only pretraining.

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.

While multi-agent reinforcement learning (MARL) has been proven effective across both collaborative and competitive tasks, existing algorithms often struggle to scale to large populations of agents. Recent advancements in mean-field (MF) theory provide scalable solutions by approximating population interactions as a continuum, yet most existing frameworks focus exclusively on either fully cooperative or purely competitive settings. To bridge this gap, we introduce MF-MAPPO, a mean-field extension of PPO designed for zero-sum team games that integrate intra-team cooperation with inter-team competition. MF-MAPPO employs a shared actor and a minimally informed critic per team and is trained directly on finite-population simulators, thereby enabling deployment to realistic scenarios with thousands of agents. We further show that MF-MAPPO naturally extends to partially observable settings through a simple gradient-regularized training scheme. Our evaluation utilizes large-scale benchmark scenarios using our own testing simulation platform for MF team games (MFEnv), including offense-defense battlefield tasks as well as variants of population-based rock-paper-scissors games that admit analytical solutions, for benchmarking. Across these benchmarks, MF-MAPPO outperforms existing methods and exhibits complex, heterogeneous behaviors, demonstrating the effectiveness of combining mean-field theory and MARL techniques at scale.

Pioneering companies such as Waymo have deployed electric robo-taxi services in several U.S. cities. Operating such fleets requires coordinating ride matching, vehicle repositioning, and battery charging in a stochastic environment while accounting for limited charging infrastructure. Understanding both how to design efficient, scalable control algorithms for large fleets and how charger deployment shapes system performance is therefore critical for robo-taxi operators. We model the operations of an electric robo-taxi system as a discrete-time Markov decision process with a long-run average reward objective. To efficiently evaluate system performance under different configurations, we develop a scalable deep reinforcement learning algorithm, Atomic Proximal Policy Optimization (Atomic-PPO), which reduces the action space using atomic action decomposition. The resulting training procedure requires only modest computational resources, making it practical to evaluate a large number of system configurations. We calibrate a simulation environment using real-world NYC for-hire vehicle trip records and benchmark Atomic-PPO against heuristic policies and a fluid-based reward upper bound. The results show that Atomic-PPO produces near-optimal fleet dispatching policies and serves as a reliable tool for system evaluation. We conduct extensive numerical experiments to evaluate how charging infrastructure and fleet size affect system performance. Our findings highlight the importance of ridership-based charger placement, balanced investments in charger quantity and charging speed, and joint planning of charging infrastructure and fleet size.

Industry is moving toward autonomous, network-connected machines that detect and adapt to changing conditions, including hardware faults. Conventional fault-tolerant design duplicates hardware and reroutes control logic; reinforcement learning (RL) offers a learning-based alternative. This paper presents the first systematic comparison of two RL algorithms -- Proximal Policy Optimization (PPO) and Soft Actor-Critic (SAC) -- for integrating fault tolerance into control. Beyond algorithm choice, we investigate four knowledge-transfer strategies: retaining or discarding model parameters, and retaining or discarding storage contents. Performance is evaluated in two Gymnasium environments: Ant-v5 and FetchReachDense-v3. Results show rapid, fault-specific recovery with clear trade-offs. In Ant-v5, retaining PPO's parameters boosts early returns and remains the safest choice across all faults, while retaining SAC's parameters yields mixed outcomes. SAC's early performance further depends on whether the replay buffer is retained: beneficial when prior experiences match current dynamics, but harmful when they diverge. In FetchReachDense-v3, discarding both PPO's and SAC's parameters was most effective under sensor corruption. Across tasks, both algorithms recover near-normal performance within minutes in low-dimensional settings and within days in high-dimensional settings, highlighting a clear trade-off between adaptation speed and asymptotic performance. These findings demonstrate that RL can deliver robust fault tolerance and offer practical guidelines.

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.