Model-Free RL

LLM-guided program evolution has enabled discoveries in mathematics and computational optimization, raising the prospect of reinforcement learning (RL) algorithms that self-evolve to improve how agents learn. However, realizing this prospect faces two obstacles. Joint search over coupled algorithmic components is difficult to scale: simultaneous changes can disrupt learning, while isolated changes overlook their dependencies. Evaluating candidate algorithms also requires costly training, with fitness remaining uncertain across random seeds. We introduce RLDiscover, a framework for the self-evolution of model-free deep RL algorithms. Progressive Co-Evolution advances from targeted component edits to joint evolution, while Progressive Probabilistic Evaluation balances search breadth and evaluation fidelity through staged training and repeated evaluation. Experiments across SAC, PPO, and DQN on four benchmark suites show substantial improvements in mean return, with per-family median gains of 32%-84% and a peak return ratio of approximately 363x over a near-zero baseline. These gains include transitions from failed learning to successful task completion, and improvements persist when evolution starts from stronger open-source implementations. On measured SAC locomotion runs, evaluation uses approximately one-fifteenth the estimated compute required to fully evaluate the same candidate pool. Remarkably, independent searches repeatedly discover interpretable combinations of adaptive robust losses, progress-dependent value targets, and running statistics, with selected programs transferring to unseen tasks. These findings point toward a broader role for self-evolution in AI: discovering interpretable algorithms that improve how agents learn.

Diffusion policies provide expressive action distributions for continuous-control reinforcement learning. However, safety-aware online diffusion policy optimization remains underexplored, particularly methods that use predictive reachability information without an explicit dynamics model. We propose Reachability-Aware Diffusion Policy Optimization (RADPO), a model-free method that combines predictive first-hit safety estimation with cumulative-cost budget feedback. RADPO learns a discounted first-hit reachability value that captures the discounted risk of a cost event, assigns larger weight to events that occur sooner, and uses this signal to shape the reward. A separate dual-like multiplier adjusts the shaping strength according to realized episodic costs relative to a prescribed budget. The diffusion actor improves through weighted denoising regression on candidate actions scored by the reward critic. Our approach requires neither a learned dynamics model, action gradients through the critics, nor differentiation through the reverse diffusion sampler. We establish theoretical properties of the reachability value and show that accumulated reachability penalty provides a conservative surrogate for future discounted cumulative cost. Across ten continuous-control safety tasks, RADPO achieves competitive reward-cost trade-offs, with substantial reductions in constraint violations on several tasks relative to the compared baselines. Our theoretical and empirical analysis supports that combining reachability with cumulative budget feedback is a viable approach to safety-aware diffusion policies.

In Networked Markov Decision Processes, transition dynamics are often unknown and the state--action space grows rapidly with the number of agents. In this setting, Taylor representations naturally approximate $Q$-functions, but a naive order-$n$ expansion over $N$ agents requires $Θ(N^n)$ coefficients. We justify these expansions under smooth expected future local rewards with controlled derivatives. Under this condition, finite-speed information propagation and discounting imply that local-critic Taylor coefficients decay exponentially with the graph distance to the farthest agent involved. Discarding distant-agent coefficients and marginalizing then yield scalable local Taylor representations with a bound controlled by graph locality. Building on these representations, we propose a scalable model-free actor--critic algorithm, establishing finite-sample critic and near-stationarity guarantees for a linear LSTD critic. We then introduce a more expressive neural TD parameterization. Unlike prior constructive spectral methods, our approach covers settings without access to a known local dynamics map, such as hidden switched linear--quadratic regulation. Across three control benchmarks, our method matches or outperforms spectral baselines while scaling efficiently to large graphs.

Reinforcement learning (RL) for reachability specifications is fundamental to sequential decision-making. Prior work establishes asymptotic convergence to optimal policies, but only through model-based methods that must explicitly estimate the transition probabilities of the underlying Markov Decision Process (MDP). We present Quasar, the first model-free algorithm with asymptotic guarantees for reachability on the fragment of MDPs free of non-terminal maximal end components (MECs), a building block to which every MDP reduces by the standard MEC quotient. Our algorithm follows the classical Q-learning approach, using temporal-difference updates to converge to an optimal policy without ever learning the transition probabilities. The resulting learner reduces the memory footprint from the O(|S|^2|A|) that model-based methods require to O(|S||A|). On the standardized Quantitative Verification Benchmark Set, our algorithm converges to the optimal policy with orders of magnitude fewer samples than the previous model-based state-of-the-art. Together these results are a concrete step toward the practical deployment of reachability learning and, with it, of specification-guided RL.

Principled exploration in reinforcement learning requires an agent to quantify its epistemic uncertainty and act to resolve it. Uncertainty over the value function provides a natural signal for exploration, yet existing deep approximations remain brittle and perform inconsistently. The central challenge is therefore to scale these ideas robustly. We conduct a systematic empirical study of how epistemic uncertainty is represented, propagated, and optimized in deep epistemic value functions, and uncover distinct failure modes along each of these axes. These findings motivate DEVOTE, a model-free reinforcement learning algorithm that controls how uncertainty generalizes beyond observed data, stabilizes its temporal propagation, and preserves adaptation to the resulting non-stationary exploration objective. Across reward-free exploration and challenging continuous-control tasks, DEVOTE reaches novel states more effectively and achieves higher task return than strong model-free and model-based exploration baselines. These results provide evidence that deep epistemic value functions are a promising path toward scalable, principled exploration.

Group-based reinforcement learning (RL) has advanced large language models (LLMs) and is increasingly extending to agentic tasks, where sparse terminal rewards make step-level credit assignment essential. Existing methods assign credit from what follows an action in sampled rollouts, but do not explicitly capture its retrospective relation to the realized outcome. Hindsight credit assignment (HCA) instead attributes credit through the ratio of hindsight to behavior-policy probabilities, but estimating the hindsight distribution requires an auxiliary model or an extra pass. To address this estimation bottleneck, we propose GraphHCA, a model-free realization of HCA that eliminates explicit hindsight-distribution estimation. For terminal-goal tasks with deterministic transitions, Bayes' rule reduces the hindsight ratio to a ratio of behavior-policy success probabilities at consecutive states. Taking logs yields a state-wise success potential, whose increment across a transition provides step-level credit. GraphHCA estimates this potential from pooled rollouts through a discounted recursion on the induced transition graph, which admits a unique fixed point on any directed graph. The resulting step-level signal is combined with the trajectory-level advantage, requiring neither a learned hindsight model nor an extra forward pass and recovering GRPO when the step-level weight is zero. Among all compared baselines, GraphHCA achieves state-of-the-art results on ALFWorld and WebShop at both LLM scales, and on Sokoban with a vision-language agent. For example, on ALFWorld it improves overall success rate by up to 24.6 points over GRPO and by up to 4.7 points over the strongest step-level baseline.

Offline reinforcement learning (RL) typically trains a critic by minimizing a regression loss against bootstrapped value targets stabilized by target networks with exponential moving average (EMA) updates. Multi-step targets incorporate behavior-policy actions and therefore require off-policy correction. We instead impose in-sample Bellman optimality on the critic through inequality constraints. We formulate the Lifted Bellman Linear Program (LBLP), which lifts the linear programming characterization of Bellman optimality to the joint $(Q,V)$ space so that every constraint involves only state-action pairs in the dataset. Its unique minimizer is the in-sample optimal pair, and constraints along $K$-step segments of dataset trajectories leave this minimizer unchanged for any rollout policy and horizon. Under deterministic dynamics, this minimizer lies between the best dataset return and the optimal value. Relaxing the constraints into hinge penalties recovers the same solution above a finite penalty coefficient in the tabular case. Approximate Lifted Bellman Unconstrained Minimization (ALBUM) implements this relaxation with neural networks and detaches the $K$-step rollout targets by stop gradient. Its objective contains no squared regression onto bootstrapped targets, so it can be trained without target networks or EMA updates. Under deterministic dynamics, the LBLP solution is a stationary point of the detached update under a coefficient condition independent of $γ$ and $K$, and the inequality constraints allow discounted returns along dataset trajectories to serve as lower bounds without off-policy correction or action chunking. On OGBench, ALBUM uses a single critic with a Gaussian policy, matches the average performance of FQL, and is comparable to recent action-chunking methods, while using the fewest parameters and the least peak GPU memory among all compared methods.

Deep Reinforcement Learning (RL) is notoriously sample inefficient. One contributing factor is that RL agents are typically initialized from scratch, forcing them to acquire task-relevant knowledge through online interaction. Existing approaches obtain informative initializations through pre-collected datasets, high-fidelity simulators, or meta-learning over related tasks, but these prerequisites may be difficult to access or even unavailable. In this paper, we propose Programmatic Dynamics Priors for Value Network Initialization (ProDVI), a framework that leverages the commonsense and domain knowledge encoded in large language models to initialize RL agents without relying on these resources. Specifically, ProDVI prompts a code-generating language model to produce executable Python functions that encode coarse hypotheses about environment dynamics. These functions are then used to generate synthetic transitions. Based on these transitions, we construct an auxiliary dynamics prediction objective to pretrain the state-action encoder of the value network in an actor-critic framework. The learned representation provides dynamics-aware inductive biases before online RL begins. Importantly, the generated programs are used only for representation pretraining and are not required to faithfully simulate the target environment. While the generated programs may be inaccurate, their induced initialization can be corrected through online learning from real transitions and rewards. Experiments on OpenAI Gym and DeepMind Control Suite tasks show that ProDVI can effectively improve the sample efficiency of model-free RL algorithms.

Sample-efficient policy learning from pixels is a long-standing challenge in reinforcement learning (RL). Recent dynamics-based representation learning methods have significantly improved the sample efficiency of model-free visual RL by learning dynamics-aware representations through auxiliary prediction performed either in latent space (self-prediction) or observation space (observation prediction). However, state-of-the-art methods from both categories still struggle on challenging visual control tasks when training data is limited. We posit that relying on either predictive objective alone may be insufficient. In contrast, observation prediction grounds learned representations in observation-level dynamics, but does not directly regularize the temporal predictability of latent representations over extended horizons. In this paper, we propose Observation-Grounded Self-Predictive Representations (OG-SPR), a model-free visual RL algorithm for continuous control that learns representations that are both temporally predictive in latent space and grounded in observation-level dynamics. OG-SPR incorporates two core auxiliary objectives: multi-step latent self-prediction and next-observation prediction. We empirically show that directly imposing latent self-prediction on the shared representation may over-constrain it and does not necessarily improve performance. To address this issue, OG-SPR introduces two lightweight adapters for latent self-prediction, allowing the shared representation to benefit from temporally predictive signals without being forced to directly satisfy the self-prediction objective. Experiments on 28 visual control tasks from the DeepMind Control Suite show that OG-SPR improves aggregate performance over state-of-the-art self-predictive and observation-predictive RL methods, with particularly pronounced gains in challenging domains such as dog and humanoid.

This work studies model-free reinforcement learning for co-safe linear temporal logic (sc-LTL) objectives in finite Markov decision processes, which can be reduced to maximal reachability objectives via the standard product construction. For this problem, direct sample-based bootstrap methods (e.g., TD or Q-learning) may fail to converge to optimal policies due to the noncontractive nature and nonuniqueness of solutions to the Bellman equation. We develop a new two-step model-free reinforcement learning method that first uses a discounted surrogate to identify a clamp set that resolves this nonuniqueness, and then applies undiscounted policy evaluation and greedy policy improvement with guarantees of finding an optimal solution. We prove almost-sure convergence of the policy evaluation step and finite termination of the policy iteration algorithm at an optimal policy. These theoretical results are validated through numerical experiments on a stochastic grid world.

Discounted exponential utility provides a principled criterion for risk-sensitive sequential decision-making, but its nonlinear structure complicates reinforcement learning. A recent work \citep{thoppe2026reinforcement} addressed this difficulty by introducing a Bellman-compatible surrogate and two model-free fixed-point algorithms for optimizing it over stationary policies. However, their main convergence results are asymptotic. In this work, we establish finite-time rates of $\tilde{O} (1/\sqrt{n})$ for the aforementioned two algorithms under asynchronous Markovian sampling, where $n$ is the iteration index and $\tilde{O}$ hides logarithmic expressions. Importantly, we employ parameter-free choices for the stepsize parameter to derive these rate results. For the algorithmically simpler one-timescale method, the main challenge is that its update equation is not directly aligned with the contraction geometry of its underlying power-law operator. We overcome this mismatch by exploiting the boundedness, monotonicity, and homogeneity of the operator to obtain a local pseudo-contraction property for the relative-error dynamics. We then use a Moreau-envelope-based Lyapunov function and Polyak--Ruppert averaging to obtain the stated convergence rate with parameter-free stepsizes. For the two-timescale method, the main challenge is to control a tracking error on the faster timescale. These results provide the first finite-time guarantees for model-free discounted exponential-utility reinforcement learning.

Multi-zone variable-air-volume control must balance thermal comfort, indoor air quality, and electricity use across several continuous actuators. Model predictive control and reinforcement learning are widely studied, but deployment typically requires building-specific modeling or training, limiting scalability. We first test whether a frontier reasoning model (an LLM trained to use additional inference-time computation) can achieve competitive VAV control from text without building-specific training. With that capability established, we then test whether TD3-guided reinforcement fine-tuning (RFT) can transfer control knowledge into a locally deployable open-weight model. Five controllers are evaluated over three summer days in a physics-based four-zone emulator. Relative to a Guideline 36-based baseline, TD3 reduced HVAC electricity by 4.5% while improving temperature and CO$_2$ compliance. Without building-specific training, GPT-5 achieved the largest reduction (6.2%) but reduced the ventilation margin. For RFT, deterministic rollouts restore a saved state, apply one candidate, and follow TD3 to score each action. Auditing a learned critic against these rollouts exposed a failure hidden by its near-perfect across-time correlation ($r=0.9998$): within-state ranking was unreliable; the critic selected the rollout-best candidate in only 5 of 10 states. Even with the rollout verifier, 200 RFT steps produced no sustained improvement in sampled-action return; the open-weight controller used more electricity than the baseline before and after training, and its five-minute predictions remained worse than persistence. GPT-5 predicted transitions far better. Exact rollout scores rank sampled actions but reveal neither next-state effects nor an improvement direction. The unchanged transition errors motivate transition-focused supervised fine-tuning before value-based RFT.

Unmanned aerial vehicles (UAVs), particularly quadcopters, present unique challenges for autonomous control due to their underactuated dynamics: only four available control inputs must govern six degrees of freedom. This paper investigates a physics-aware, end-to-end deep reinforcement learning (DRL) approach that acts directly on low-level body inputs, total thrust and body torques $(T, τ_x, τ_y, τ_z)$, and closes the loop through a high-fidelity Simulink environment. Our simulator integrates a 12-state rigid-body model (MATLAB Level-2 S-Function) with (i) an Action2RPM allocation based on the Moore-Penrose pseudo-inverse of a coefficient matrix derived from thrust and drag terms, and (ii) first-order actuator dynamics for each motor (time constant $T_m = 0.076$ s), including rotor gyroscopic coupling. A shaped reward balances goal-reaching and stability using an exponential position well, attitude penalties, and quadratic velocity costs. Four DRL algorithms, DDPG, TD3, PPO, and SAC, are evaluated in two stages: (S1) thrust-only hover and (S2) hover with pitch torque and a translated goal. Results show that SAC and TD3 achieve superior stability and exploration efficiency, while PPO is less sample-efficient. The study highlights the significance of modeling actuator lags and aerodynamic moments for stable low-level control and provides a reproducible benchmark for quadcopter DRL.

Reinforcement learning is conventionally divided into model-based and model-free methods. In this taxonomy, model-based methods perform lookahead planning over a learned world model, whereas model-free methods learn a reactive state-action mapping. Recent work, however, has shown that planning can emerge from model-free reinforcement learning alone. The conditions under which this behavior emerges from a pure reward-maximization objective have so far remained unclear. In this paper, we present evidence that, in the observed cases, the hidden-state structure of the neural architecture is the deciding factor. We find that a network of relational hidden states, each anchored to an environment state and exchanging messages along learned relations, acquires a planning mechanism. These hidden states recover the environment's transition structure in their learned relations, and improve the policy at decision time by planning over the learned graph. In a matched control agent that must additionally discover which cells represent which states, no such binding arises, and no planning follows from it. We argue that this explains the observed phenomenon of emergent planning in model-free reinforcement learning and raises the question of how common such emergent planning might be more generally. Finally, we hypothesize that the discovered mechanism could describe how planning emerges from pure reward maximization in the human brain through a neural architectural prior.

Across environments with mixed sources of uncertainty, unsupervised reinforcement learning requires intrinsic motivation that does not precommit to a particular direction of surprise. Surprise minimization is scoped by design to ``unstable'' environments. Prediction-error curiosity rewards total expected surprise, including irreducible noise. Bandit or mixture switching between surprise-minimizing and surprise-maximizing rewards reintroduces non-stationarity by construction. We propose a single intrinsic reward, stationary within each window, derived from the novelty contribution of a preference-free Expected Free Energy objective, expressed in reward-maximization form. Our claim is that parameter information gain, the expected surprise of the next state minus its irreducible part, is the appropriate intrinsic signal in both high-entropy and low-entropy components of the state space. Maximizing it seeks exactly the surprise the model can explain away. In regions of unresolved dynamics, this epistemic term drives exploration. As dynamics become resolved, the epistemic term vanishes, while an aleatoric penalty favors lower-variance transitions, all without fitting an explicit next-state predictor. A pseudocount supplies epistemic value, a probe-based penalty captures aleatoric variance, and a short-horizon gate protects informative successors. A window-based freeze of all reward-defining objects yields a stationary Bellman operator, explicit bounds on learning targets, and a conditional uniform-concentration result for the nonparametric estimators under mixing, smoothness, bandwidth, and capacity assumptions. In active-inference terms, the agent is preference-free where novelty is retained, standard likelihood ambiguity vanishes under full observability, a nonstandard transition-entropy penalty is added, and surprise minimization emerges in resolved regions of the state space.

This paper develops a model-free reinforcement learning framework for continuous--time extended mean field control problems, where both the dynamics and reward may depend on the joint distribution of states and controls. We adopt deterministic feedback policies, under which the state--action distribution is induced directly as a push--forward of the state law. This avoids optimization over stochastic kernels and bypasses key limitations of existing approaches in extended mean field settings. We first establish a model--free sensitivity formula for parameterized McKean--Vlasov dynamics and use it to derive a deterministic policy gradient formula expressed through an advantage--rate function on the Wasserstein space. We then refine this formula by introducing local value and advantage--rate representations that depend on the state, action, and joint state--action distribution, yielding a policy gradient that includes both action derivatives and measure--derivative terms with respect to the control distribution. These characterizations lead to a martingale--based learning principle and motivate a continuous--time deep deterministic policy gradient algorithm combining particle approximations, measure--dependent neural networks, temporal--difference learning, and exploration in either action or parameter space. Numerical experiments on stochastic Cucker--Smale consensus control and optimal liquidation with trade crowding demonstrate the efficiency, stability, and robustness of the proposed method, including problems with explicit dependence on the control distribution.

In this paper, we investigate whether a model-free RL agent can identify and exploit price manipulation opportunities more effectively than a traditional model-based approach that assumes correct specification of the data-generating process but relies on noisy parameter estimates. We consider a single-asset market in which prices evolve according to an Almgren-Chriss framework with non-linear permanent impact and linear temporary impact. We first establish the existence of price-manipulative strategies in discrete time and compute the optimal benchmark strategy using Sequential Least Squares Quadratic Programming under full information. We then compare two finite-sample learning approaches: a model-based procedure that estimates impact parameters from simulated execution data and an agnostic RL approach based on Deep Deterministic Policy Gradient, trained directly on the same amount of data. For intermediate volatility, the RL agent successfully discovers profitable manipulative strategies without explicit knowledge of the underlying model, even when training data are quite limited. More importantly, RL consistently outperforms the model-based approach when parameter estimates are affected by sampling error, despite the latter benefiting from the correct model specification. For large volatility, all methods are unable to identify manipulation opportunities, while for small volatility, the model based approach outperforms RL. These findings highlight both the effectiveness of RL in complex control problems and the risks associated with deploying learning algorithms in financial markets without appropriate safeguards.

This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition data are available. In the model-based formulation, policy evaluation is naturally described by a stationary Hamilton-Jacobi-Bellman equation on $\mathcal P_2(\mathbb R^d)$, but this equation involves the drift and diffusion coefficients of the controlled McKean-Vlasov dynamics, which are not identifiable when only discrete-time data are available. On the other hand, a direct reduction to a time-discrete Bellman equation avoids the non-identifiability issue but loses the differential equation structure. To bridge these two viewpoints, we introduce a Mean-Field-PhiBE (MF-PhiBE), which incorporates discrete-time transition information into a continuous-time PDE on the Wasserstein space. The MF-PhiBE replaces the unknown infinitesimal drift and covariance in the policy-evaluation equation by one-step estimators computed from data, while preserving the generator structure of the McKean-Vlasov HJB equation. We also derive a policy-gradient theorem for entropy-regularized randomized feedback policies, expressing the actor direction through an action-wise infinitesimal advantage and the score of the policy. Combining these two ingredients yields a model-free actor-critic method. We prove a first-order consistency estimate showing that the value induced by an optimal MF-PhiBE policy approximates the optimal continuous-time value with an error of order $Δt$. In the linear-quadratic case, we show our approximation achieves second-order accuracy with only one-step data. Numerical experiments on an LQR benchmark and a crowd-aversion problem illustrate the proposed framework.

In recent years, the Internet of Things (IoT) paradigm has been shifting toward batteryless, energy-harvesting architectures. Sustaining reliable operation in these systems requires intelligent management of highly volatile stored energy. As edge applications grow in complexity, traditional energy-aware schedulers struggle with unpredictable workloads due to their reliance on static execution thresholds or pre-measured, hardware-specific task profiles. To overcome this, we propose two novel, hardware-agnostic dynamic scheduling strategies treating applications as a "black box," requiring no prior energy information: a model-free Reinforcement Learning (RL) agent and an on-the-fly Approximated Prediction (AP) method. We evaluate these methods against an adaptive task rate approach (AsTAR) and optimized static thresholds using a custom-built, physically accurate simulation framework driven by real-world solar data and dynamic LoRa transmission profiles. Rather than claiming universal superiority, our analysis exposes the distinct operational trade-offs of each method: the AP approach delivers lightweight, near-oracle task throughput; the RL agent provides tunable survival-execution balancing; and AsTAR excels at execution pacing across long energy gaps. Finally, we demonstrate that while these advanced strategies provide critical resilience for severely constrained systems with small capacitors, devices with larger energy buffers can efficiently rely on simpler, less computationally expensive static policies.

Augmenting model-free reinforcement learning (RL) with representations learned through observation dynamics prediction (observation-predictive RL) can improve sample efficiency and performance, with minor modifications and limited additional computation. However, this approach still struggles in challenging tasks with low-dimensional observations. In this paper, we identify a key factor behind this problem: unbalanced reconstruction losses across observation dimensions, where dimensions with larger value ranges dominate the loss. This encourages the agent to neglect dimensions with relatively small ranges, leading to degraded performance. To address this issue, we propose a novel normalization method tailored to online RL, which normalizes low-dimensional observations and balances the resulting losses and gradients. Beyond balancing reconstruction losses, observation normalization enables dynamics prediction to be performed in a normalized observation space, thereby providing a unified treatment of low- and high-dimensional inputs (e.g., physical states and images). Building on this idea, we further introduce Normalized Observation Space Dynamics-Augmented Q-learning (NASDAQ), a framework for observation-predictive RL applicable across diverse domains. NASDAQ learns state-action representations by coupling value learning with two auxiliary tasks: short-term value prediction and next normalized observation prediction. Extensive experiments demonstrate that NASDAQ achieves competitive or superior performance compared with state-of-the-art model-based and self-predictive RL methods, while requiring significantly less training wall-time.

Model-based and model-free reinforcement learning are traditionally viewed as separate paradigms: instead of learning a model of the transition kernel $P$, model-free agents typically estimate value functions tied to a specific policy and reward. In this paper, we challenge this dichotomy by proving that value-based agents trained on a sufficiently rich set of reward functions, e.g. using goal-conditioned RL, implicitly encode a unique and accurate world model. To extract this model in practice, we introduce \textit{$P$-learning}, an inverse analogue to $Q$-learning that samples from an agent's $Q$-values, policies and rewards to decode its internal model of the environment. We then provide sufficient conditions on the type and number of goals for which agents encode the true kernel $P$, covering both stochastic and deterministic MDPs over finite or continuous state spaces. Even when our assumptions are violated, we empirically demonstrate that agents trained on a handful of reward functions encode accurate dynamics in $\texttt{Reacher}$, $\texttt{MountainCar}$ and stochastic variants of $\texttt{FourRooms}$. Surprisingly, we find that policies trained exclusively on a \texttt{Reacher} agent's implicit world model are quasi-optimal on out-of-distribution, velocity-based goals despite position-only training -- suggesting that agents contain hidden generalisation capabilities and providing a new lens into the connection between model-based, model-free, and goal-conditioned RL.

This paper compares the performance of model-free controllers on a nonlinear system under cyberattacks, including false data injection and denial-of-service attacks. Four RL reward types are analyzed for accuracy, cost, and resilience. Results show that the Lyapunov reward offers the best resilience with low tracking error. Exponential mode also provides good trade-offs with acceptable resilience under moderate training conditions. Progressive and linear rewards converge faster but are less robust. RL-MPCs show strong steady-state resilience but require longer training times; RL-PID controllers are faster with significantly less training time. Proximal Policy Optimization outperforms Deep Deterministic Policy Gradient with a significant reduction in KPI variance. This study serves to highlight how well-designed RL rewards can improve performance and resilience against cyber threats.

While there is an extensive body of work characterizing the sample complexity of discounted cumulative-reward MDPs, finite sample analyses for average-reward MDPs have been limited, and most existing works rely on restrictive assumptions such as ergodicity or access to a generative model. In this work, we establish the first finite sample complexity guarantees from a single trajectory for weakly communicating average-reward MDPs. To this end, we study the dynamics of a single trajectory in weakly communicating MDPs and based on this analysis, we develop novel model-free methods. Notably, our value-based and policy-based methods provide finite sample complexity guarantees of $\widetilde{O}(1/\varepsilon^2)$ and $\widetilde{O}(1/\varepsilon^4)$ from a single trajectory in weakly communicating MDPs, respectively. Furthermore, we introduce the first model-free method that requires no prior knowledge of problem-dependent quantities for communicating MDPs.

In this paper, we develop a continuous-time model-free reinforcement learning algorithm to learn deterministic equilibrium policies in general time-inconsistent control problems. Utilizing the extended Hamilton-Jacobi-Bellman system, we recast the original time-inconsistent problem into an equivalent two-stage problem. In the first stage, for given auxiliary functions, we employ the deterministic policy gradient approach to learn an optimal policy in an auxiliary time-consistent control problem. In the second stage, given the updated policy, we exploit the inner fixed point iterations and some martingale characterizations to learn the auxiliary functions. As a theoretical contribution, we provide some mild model assumptions and establish the convergence of inner fixed point iterations. By repeating this actor-critic style of iterations across two stages, our algorithm aims to learn the equilibrium under different sources of time-inconsistency in a unified manner. The superior effectiveness of the proposed algorithm are illustrated in two classical financial applications with time-inconsistency: mean-variance portfolio management and optimal tracking portfolio under non-exponential discounting.

Reinforcement learning promises to optimize sequential decisions in large-scale systems. Semiconductor manufacturing systems are stochastic and highly constrained environments where heterogeneous wafers traverse hundreds of processing steps across extensive equipment networks. These characteristics yield complex, high-dimensional decision problems with delayed feedback and long-horizon requirements, complicating production planning and control. We propose a deep reinforcement learning framework for multi-objective policy optimization at this scale. Specifically, we formulate control as a centralized-agent problem, where a core policy coordinates system-wide decisions, while system evolution is represented as an interconnected temporal process driven by discrete events. Accordingly, we develop a tailored event-driven temporal-difference formulation that remains general and can be integrated with various policy optimization methods under relevant training settings. We investigate several core model-free algorithms incorporated into this framework and evaluate their effectiveness using high-fidelity simulations of diverse, industry-real operating scenarios. Across extensive validation experiments, agents trained in both offline and online settings show significant and consistent gains in throughput and utilization. We further evaluate performance and generalization across training phases, clarifying the relative strengths of alternative reinforcement learning formulations and algorithms. Overall, the results support the scalability, generality, and transferability of the proposed framework for controlling event-driven complex adaptive systems.

Training reinforcement learning (RL) policies from scratch is costly: it requires careful reward and environment design, extensive tuning, and substantial computation. Yet many control problems already have a functional but suboptimal policy available as a baseline. This paper proposes a method for embedding such a baseline into the RL training process, simultaneously improving training efficiency relative to from-scratch methods and producing a learning policy that outperforms the baseline. At each step, the method arbitrates between the baseline policy and a trainable learning policy, initially relying strongly on the baseline policy and then progressively transferring agency to the learning policy. By the end of training, the learning policy is a standalone neural network that operates without baseline policy support. The paper formalizes what it means for the baseline policy to be functional: under this policy, the agent reaches a goal set and remains there with high probability. The proposed arbitration mechanism is designed to exploit this property during training, yielding high goal-reaching rates right from the beginning of training. A theoretical analysis provides a formal interpretation of this behavior under stated assumptions and extends it to the final baseline-free regime, where explicit lower bounds are derived for the goal-reaching probability of the standalone learning policy. Empirical results on continuous-control benchmarks show that the proposed method achieves returns that match or exceed those of competitive approaches, while maintaining the highest goal-reaching rates throughout training among the compared methods -- including in the final stage, where the learning policy operates without any baseline support.

Scaling reinforcement learning (RL) to diverse multitask settings remains a central challenge. While recent advances in model-based RL achieve strong performance, they rely on planning and complex training pipelines, making it unclear which components are essential for scalability. We revisit this question and argue that the primary driver of scalable multitask RL is not model-based control, but \emph{representation learning}. In particular, we show that combining predictive, model-based representations with high-capacity value function approximation is sufficient to achieve strong performance, even without planning. We evaluate a simple model-free algorithm, MR.Q, coupled with auxiliary predictive objectives into a scalable actor-critic architecture. This approach outperforms a recent world-model-based method and a range of deep RL baselines across a diverse suite of multitask continuous control tasks, while significantly reducing computational overhead and improving wall-clock efficiency. We observe consistent improvements with increased model capacity and show through ablations that predictive representation learning is critical for performance.

It has been proposed that the brain integrates flexible, computationally expensive cortical processing with simpler, lower-cost subcortical mechanisms to achieve resource-efficient performance greater than that of either system alone. Despite the allure of this perspective, satisfying theoretical frameworks that explore this hypothesis are still limited. We extend existing frameworks in which a model-based module and model-free module learn in tandem by explicitly constraining the memory resources of the model-based module, and investigate the impact of this constraint in a simple decision-making setting. Memory constraints naturally give rise to strategies for allocating memory resources. We evaluate the performance of different strategies in different situations and demonstrate that when the rewarded states change often, it can be advantageous for the model-based module to focus its memory resources not on exploiting the current reward, but on capturing general structure of the environment. This work provides a theoretical foundation for a functional dissociation between cortical and subcortical systems during learning: the cortex supports general structure learning, while subcortical circuits specialize in reward-based learning. We further detail how these hypotheses can be tested on experimental data.

We study model-free Q-learning in finite-horizon episodic Markov Decision Processes (MDPs) with stationary dynamics across episodes. We identify a central issue in nascent model-free posterior-sampling works: the reliance on delayed learning in order to prove theoretical guarantees. In particular, we identify three opportunities for faster learning - (i) value-function update order, (ii) update frequencies, and (iii) value-function initialization. Using Wang et al.'s RandomizedQ as a basis, we illustrate these changes and their individual (as well as cumulative) impact in multiple empirical studies. We find that our combined modifications, termed ReversedQ, improve scaled mean cumulative reward compared to RandomizedQ, from 9.53% to 78.78% in the Bidirectional Diabolical Combination Lock (BDCL), and from 21.76% to 61.81% in a chain MDP.

We propose a model-free offline multi-step reinforcement learning (RL) algorithm, Conservative Peng's Q($λ$) (CPQL). Our algorithm adapts the Peng's Q($λ$) (PQL) operator for conservative value estimation as an alternative to the Bellman operator. To the best of our knowledge, this is the first work in offline RL to theoretically and empirically demonstrate the effectiveness of conservative value estimation with a \textit{multi-step} operator by fully leveraging offline trajectories. The fixed point of the PQL operator in offline RL lies closer to the value function of the behavior policy, thereby naturally inducing implicit behavior regularization. CPQL simultaneously mitigates over-pessimistic value estimation, achieves performance greater than (or equal to) that of the behavior policy, and provides near-optimal performance guarantees -- a milestone that previous conservative approaches could not achieve. Extensive numerical experiments on the D4RL benchmark demonstrate that CPQL consistently and significantly outperforms existing offline single-step baselines. In addition to the contributions of CPQL in offline RL, our proposed method also contributes to the offline-to-online learning framework. Using the Q-function pre-trained by CPQL in offline settings enables the online PQL agent to avoid the performance drop typically observed at the start of fine-tuning and to attain robust performance improvements. Our code is available at https://github.com/oh-lab/CPQL.