Actor-Critic Methods

Although actor-critic methods have been successful in practice, their theoretical analyses have several limitations. Specifically, existing theoretical work either sidesteps the exploration problem by making strong assumptions or analyzes impractical methods with complicated algorithmic modifications. Moreover, the actor-critic methods analyzed for linear MDPs often employ natural policy gradient and construct "implicit" policies without explicit parameterization. Such policies are computationally expensive to sample from, making the environment interactions inefficient. To that end, we focus on the finite-horizon linear MDPs and propose an optimistic actor-critic framework that uses parametric log-linear policies. In particular, we introduce a tractable $\textit{logit-matching}$ regression objective for the actor. For the critic, we use approximate Thompson sampling via Langevin Monte Carlo to obtain optimistic value estimates. We prove that the resulting algorithm achieves $\widetilde{\mathcal{O}}(ε^{-4})$ and $\widetilde{\mathcal{O}}(ε^{-2})$ sample complexity in the on-policy and off-policy setting, respectively. Our results match prior theoretical work in achieving the state-of-the-art sample complexity, while our algorithm is more aligned with practice.

Analog design often slows down because even small changes to device sizes or biases require expensive simulation cycles, and high-quality solutions typically occupy only a narrow part of a very large search space. While existing optimizers reduce some of this burden, they largely operate without the kind of judgment designers use when deciding where to search next. This paper presents an actor-critic optimization framework (ACOF) for analog sizing that brings that form of guidance into the loop. Rather than treating optimization as a purely black-box search problem, ACOF separates the roles of proposal and evaluation: an actor suggests promising regions of the design space, while a critic reviews those choices, enforces design legality, and redirects the search when progress is hampered. This structure preserves compatibility with standard simulator-based flows while making the search process more deliberate, stable, and interpretable. Across our test circuits, ACOF improves the top-10 figure of merit by an average of 38.9% over the strongest competing baseline and reduces regret by an average of 24.7%, with peak gains of 70.5% in FoM and 42.2% lower regret on individual circuits. By combining iterative reasoning with simulation-driven search, the framework offers a more transparent path toward automated analog sizing across challenging design spaces.

Reinforcement learning has proven its power on various occasions. However, its performance is not always guaranteed when system dynamics change. Instead, it largely relies on users' empirical experience. For reinforcement learning algorithms with an actor-critic structure, the critic neural network reflects the approximation and optimization process in the RL algorithm. Analyzing the performance of the critic neural network helps to understand the mechanism of the algorithm. To support systematic interpretation of such algorithms in dynamic control problems, this work proposes a critic match loss landscape visualization method for online reinforcement learning. The method constructs a loss landscape by projecting recorded critic parameter trajectories onto a low-dimensional linear subspace. The critic match loss is evaluated over the projected parameter grid using fixed reference state samples and temporal-difference targets. This yields a three-dimensional loss surface together with a two-dimensional optimization path that characterizes critic learning behavior. To extend analysis beyond visual inspection, quantitative landscape indices and a normalized system performance index are introduced, enabling structured comparison across different training outcomes. The approach is demonstrated using the Action-Dependent Heuristic Dynamic Programming algorithm on cart-pole and spacecraft attitude control tasks. Comparative analyses across projection methods and training stages reveal distinct landscape characteristics associated with stable convergence and unstable learning. The proposed framework enables both qualitative and quantitative interpretation of critic optimization behavior in online reinforcement learning.

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.

Despite remarkable achievements in single-agent offline reinforcement learning (RL), multi-agent RL (MARL) has struggled to adopt this paradigm, largely persisting with on-policy training and self-play from scratch. One reason for this gap comes from the instability of non-linear value decomposition, leading prior works to avoid complex mixing networks in favor of linear value decomposition (e.g., VDN) with value regularization used in single-agent setups. In this work, we analyze the source of instability in non-linear value decomposition within the offline MARL setting. Our observations confirm that they induce value-scale amplification and unstable optimization. To alleviate this, we propose a simple technique, scale-invariant value normalization (SVN), that stabilizes actor-critic training without altering the Bellman fixed point. Empirically, we examine the interaction among key components of offline MARL (e.g., value decomposition, value learning, and policy extraction) and derive a practical recipe that unlocks its full potential.

We study infinite-horizon Constrained Markov Decision Processes (CMDPs) with general policy parameterizations and multi-layer neural network critics. Existing theoretical analyses for constrained reinforcement learning largely rely on tabular policies or linear critics, which limits their applicability to high-dimensional and continuous control problems. We propose a primal-dual natural actor-critic algorithm that integrates neural critic estimation with natural policy gradient updates and leverages Neural Tangent Kernel (NTK) theory to control function-approximation error under Markovian sampling, without requiring access to mixing-time oracles. We establish global convergence and cumulative constraint violation rates of $\tilde{\mathcal{O}}(T^-1/4)$ up to approximation errors induced by the policy and critic classes. Our results provide the first such guarantees for CMDPs with general policies and multi-layer neural critics, substantially extending the theoretical foundations of actor-critic methods beyond the linear-critic regime.

We study policy gradient methods for continuous-action, entropy-regularized reinforcement learning through the lens of Wasserstein geometry. Starting from a Wasserstein proximal update, we derive Wasserstein Proximal Policy Gradient (WPPG) via an operator-splitting scheme that alternates an optimal transport update with a heat step implemented by Gaussian convolution. This formulation avoids evaluating the policy's log density or its gradient, making the method directly applicable to expressive implicit stochastic policies specified as pushforward maps. We establish a global linear convergence rate for WPPG, covering both exact policy evaluation and actor-critic implementations with controlled approximation error. Empirically, WPPG is simple to implement and attains competitive performance on standard continuous-control 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.

Trajectory Optimization (TO) and Reinforcement Learning (RL) offer complementary strengths for solving optimal control problems. TO efficiently computes locally optimal solutions but can struggle with non-convexity, while RL is more robust to non-convexity at the cost of significantly higher computational demands. CACTO (Continuous Actor-Critic with Trajectory Optimization) was introduced to combine these advantages by learning a warm-start policy that guides the TO solver towards low-cost trajectories. However, scalability remains a key limitation, as increasing system complexity significantly raises the computational cost of TO. This work introduces CACTO-BIC to address these challenges. CACTO-BIC improves data efficiency by biasing initial-state sampling leveraging a property of the value function associated with locally optimal policies; moreover, it reduces computation time by exploiting GPU acceleration. Empirical evaluations show improved sample efficiency and faster computation compared to CACTO. Comparisons with PPO demonstrate that our approach can achieve similar solutions in less time. Finally, experiments on the AlienGO quadruped robot demonstrate that CACTO-BIC can scale to high-dimensional systems and is suitable for real-time applications.

The dataset distributions in offline reinforcement learning (RL) often exhibit complex and multi-modal distributions, necessitating expressive policies to capture such distributions beyond widely-used Gaussian policies. To handle such complex and multi-modal datasets, in this paper, we propose Flow Actor-Critic, a new actor-critic method for offline RL, based on recent flow policies. The proposed method not only uses the flow model for actor as in previous flow policies but also exploits the expressive flow model for conservative critic acquisition to prevent Q-value explosion in out-of-data regions. To this end, we propose a new form of critic regularizer based on the flow behavior proxy model obtained as a byproduct of flow-based actor design. Leveraging the flow model in this joint way, we achieve new state-of-the-art performance for test datasets of offline RL including the D4RL and recent OGBench benchmarks.

Modern offline Reinforcement Learning (RL) methods find performant actor-critics, however, fine-tuning these actor-critics online with value-based RL algorithms typically causes immediate drops in performance. We provide evidence consistent with the hypothesis that, in the loss landscape, offline maxima for prior algorithms and online maxima are separated by low-performance valleys that gradient-based fine-tuning traverses. Following this, we present Score Matched Actor-Critic (SMAC), an offline RL method designed to learn actor-critics that transition to online value-based RL algorithms with no drop in performance. SMAC avoids valleys between offline and online maxima by regularizing the Q-function during the offline phase to respect a first-order derivative equality between the score of the policy and action-gradient of the Q-function. We experimentally demonstrate that SMAC converges to offline maxima that are connected to better online maxima via paths with monotonically increasing reward found by first-order optimization. SMAC achieves smooth transfer to Soft Actor-Critic and TD3 in 6/6 D4RL tasks. In 4/6 environments, it reduces regret by 34-58% over the best baseline.

Many real-world control problems, ranging from finance to robotics, evolve in continuous time with non-uniform, event-driven decisions. Standard discrete-time reinforcement learning (RL), based on fixed-step Bellman updates, struggles in this setting: as time gaps shrink, the $Q$-function collapses to the value function $V$, eliminating action ranking. Existing continuous-time methods reintroduce action information via an advantage-rate function $q$. However, they enforce optimality through complicated martingale losses or orthogonality constraints, which are sensitive to the choice of test processes. These approaches entangle $V$ and $q$ into a large, complex optimization problem that is difficult to train reliably. To address these limitations, we propose a novel decoupled continuous-time actor-critic algorithm with alternating updates: $q$ is learned from diffusion generators on $V$, and $V$ is updated via a Hamiltonian-based value flow that remains informative under infinitesimal time steps, where standard max/softmax backups fail. Theoretically, we prove rigorous convergence via new probabilistic arguments, sidestepping the challenge that generator-based Hamiltonians lack Bellman-style contraction under the sup-norm. Empirically, our method outperforms prior continuous-time and leading discrete-time baselines across challenging continuous-control benchmarks and a real-world trading task, achieving 21% profit over a single quarter$-$nearly doubling the second-best method.

The pretraining-finetuning paradigm has facilitated numerous transformative advancements in artificial intelligence research in recent years. However, in the domain of reinforcement learning (RL) for robot locomotion, individual skills are often learned from scratch despite the high likelihood that some generalizable knowledge is shared across all task-specific policies belonging to the same robot embodiment. This work aims to define a paradigm for pretraining neural network models that encapsulate such knowledge and can subsequently serve as a basis for warm-starting the RL process in classic actor-critic algorithms, such as Proximal Policy Optimization (PPO). We begin with a task-agnostic exploration-based data collection algorithm to gather diverse, dynamic transition data, which is then used to train a Proprioceptive Inverse Dynamics Model (PIDM) through supervised learning. The pretrained weights are then loaded into both the actor and critic networks to warm-start the policy optimization of actual tasks. We systematically validated our proposed method with 9 distinct robot locomotion RL environments comprising 3 different robot embodiments, showing significant benefits of this initialization strategy. Our proposed approach on average improves sample efficiency by 36.2% and task performance by 4.3% compared to random initialization. We further present key ablation studies and empirical analyses that shed light on the mechanisms behind the effectiveness of this method.

In-context reinforcement learning (ICRL) has emerged as an effective paradigm for test time adaptation to unseen tasks without parameter updates. However, existing ICRL methods can exhibit brittle and unstable adaptions, and the mechanisms underlying such adaptions remain poorly understood. We provide a policy-gradient view of ICRL and argue that relying on trajectory-level return feedback can lead to high-variance updates when test time rollout is limited. Motivated by the actor--critic principle, we propose Context Value Informed ICRL (CV-ICRL), which equips the in-context policy with an explicit context value: the expected discounted return conditioned on the current state and accumulated interaction context. CV-ICRL trains a value head and writes its prediction back into the context as a value token, enabling TD-style return targets for lower-variance policy updates. Experiments on the Dark Room, Minigrid, and Procgen testbeds show that CV-ICRL substantially improves the stability of test time adaptation and achieves higher returns across tasks and environments. Code and data are available at https://github.com/Bluixe/CV-ICRL .

We study model-free methods for distributionally robust infinite-horizon average-reward Markov decision processes (MDPs). We present non-asymptotic convergence analyses of Q-learning and actor-critic algorithms for robust average-reward MDPs under contamination, total-variation distance, and Wasserstein uncertainty sets. A key ingredient of our analysis is showing that the optimal robust Bellman operator is a strict contraction with respect to a carefully designed semi-norm. This property enables a stochastic approximation update that learns the optimal robust $Q$-function with $\tilde{\mathcal{O}}(ε^{-2})$ dependence on the target accuracy. We also establish robust TD convergence bounds whose constants are uniform over all stationary policies, yielding an efficient data-driven routine for robust critic estimation. Building on this, we introduce an actor-critic algorithm that learns an $ε$-optimal robust policy with $\tilde{\mathcal{O}}(ε^{-2})$ dependence on the target accuracy. We provide numerical simulations to illustrate the qualitative behavior of the proposed algorithms. Our results contribute to the theoretical foundations of robust planning under model misspecification and to model-free approaches for building robust long-run policies directly from simulation data.

Learning from a stream of experience as it arrives, also known as streaming learning, is a core part of natural learning. However, reliable streaming learning has remained a persistent challenge in modern deep reinforcement learning (RL). Instead, most deep RL algorithms learn from old experience by storing past interactions in a buffer. We show that both classical streaming RL, such as Q-learning and actor-critic, when used with deep neural networks, and batch deep RL, such as PPO, SAC, and DQN, when adapted to the streaming setting, often fail to learn. Across 58 Atari games and 50 continuous-control tasks, we find that these methods, in aggregate, perform close to random policies despite extensive task-specific hyperparameter searches. We call this pattern stream barrier. Here, we introduce Stream-X, a shared recipe for streaming deep RL algorithms that combines signal normalization, representation stabilization, and controlled parameter updates. By applying Stream-X to several base streaming RL algorithms, we provide the first family of deep RL algorithms to overcome the stream barrier. Using one prescribed hyperparameter configuration per algorithm across tasks, Stream-X substantially improves aggregate performance, often on par with batch RL algorithms. Beyond these benchmarks, we demonstrate learning with Stream-X algorithms under nonstationarity and resource constraints. Stream-AC, one of the Stream-X algorithms, repeatedly recovers performance across alternating floor-friction regimes in simulation, outperforming the evaluated PPO and SAC baselines. It also learns a heading tracking task on a robot using proprioceptive and visual features from the on-board camera in a naturally changing laboratory environment. Stream-Q learns a Pong game from pixels directly on an ESP32-S3 microcontroller, a device with limited compute and memory.

We study formal policy synthesis for continuous-state stochastic systems under linear temporal logic specifications. The product of the system with the automaton of the specification has a hybrid state space with sparse rewards. We introduce a generalized optimal backup order, defined in reverse to a topological order over automaton states, that guides value backups and provably preserves optimality. We further present a model-free actor-critic algorithm whose policy evaluation solves a constrained optimization problem by the augmented Lagrangian method, yielding hyperparameter self-tuning, and prove its optimality and convergence in the tabular case. Since integer encodings of automaton states impose a spurious ordinal relationship on functions learned by one network, we dedicate a value and a policy network to each automaton state (modular learning). The algorithm matches or outperforms PPO, DQN, and A2C on CartPole, and on a Dubins car under a temporal specification the topological order and modular learning raise the success rate from 26.0% to 71.5%.

Temporal abstraction allows reinforcement learning agents to represent knowledge and develop strategies over different temporal scales. The option-critic framework has been demonstrated to learn temporally extended actions, represented as options, end-to-end in a model-free setting. However, feasibility of option-critic remains limited due to two major challenges, multiple options adopting very similar behavior, or a shrinking set of task relevant options. These occurrences not only void the need for temporal abstraction, they also affect performance. In this paper, we tackle these problems by learning a diverse set of options. We introduce an information-theoretic intrinsic reward, which augments the task reward, as well as a novel termination objective, in order to encourage behavioral diversity in the option set. We show empirically that our proposed method is capable of learning options end-to-end on several discrete and continuous control tasks, outperforms option-critic by a wide margin. Furthermore, we show that our approach sustainably generates robust, reusable, reliable and interpretable options, in contrast to option-critic.