Model-Free RL

Event-triggered control provides a mechanism for avoiding excessive use of constrained communication bandwidth in networked multi-agent systems. However, most existing methods rely on accurate system models, which may be unavailable in practice. In this work, we propose a model-free, priority-driven reinforcement learning algorithm that learns communication priorities and control policies jointly from data in decentralized multi-agent systems. By learning communication priorities, we circumvent the hybrid action space typical in event-triggered control with binary communication decisions. We evaluate our algorithm on benchmark tasks and demonstrate that it outperforms the baseline method.

Dynamic Population Games (DPGs) provide a tractable framework for modeling strategic interactions in large populations of self-interested agents, and have been successfully applied to the design of Karma economies, a class of fair non-monetary resource allocation mechanisms. Despite their appealing theoretical properties, existing computational tools for DPGs assume full knowledge of the game model and operate in a centralized fashion, limiting their applicability in realistic settings where agents have access only to their own private experience. This paper takes a step towards addressing this gap by studying model-free equilibrium learning in Karma DPGs. First, we analyze the setting in which a novel agent joins a Karma DPG already at its Stationary Nash Equilibrium (SNE) and learns a policy via Deep Q-Networks (DQN) without knowledge of the game model. Leveraging recent convergence results for DQN, we establish a suboptimality bound consisting of a DQN approximation error of order $O(1/\sqrt{N_s})$ and a mean field perturbation error of order $O(1/N)$, where $N_s$ is the replay buffer size and $N$ is the population size. Second, we consider the challenging problem of learning the SNE from scratch. We show empirically that combining deep RL with fictitious play and smoothed policy iteration allows agents to converge, in a model-free fashion, to a configuration close to the centrally computed SNE. Together, these contributions support the vision of Karma economies as practical tools for fair resource allocation.

Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while the adversarial optimization underlying robustness makes robust evaluation computationally demanding. To address these difficulties, we consider the natural small-ambiguity regime under Kullback--Leibler ambiguity sets and propose an approximate DRRL framework based on a first-order expansion of the relevant robust functional. This yields an approximate robust Bellman equation that removes the adversarial optimization while remaining first-order accurate in the ambiguity radius. To learn the fixed point of this approximate equation, we propose Mean-Variance Stochastic Approximation (MVSA), a model-free algorithm that uses only one-sample updates. This is achieved via a lifted stochastic approximation dynamics and a two-time-scale design. We then prove convergence and a central limit theorem for MVSA: its main iterate satisfies a central limit theorem at the canonical $n^{-1/2}$ scale, with explicitly characterized asymptotic covariances. Finally, we validate our theoretical findings with a numerical experiment.

Reinforcement learning (RL) for exponential-utility optimization in discounted Markov decision processes (MDPs) lacks principled value-based algorithms. We address this gap in the fixed risk-aversion setting. Building on the Bellman-type equation for exponential utility studied in \cite{porteus1975optimality}, we derive two Q-value-style extensions and show that the associated operators are contractions in the $L_\infty$ and sup-log/Thompson metrics, respectively. We characterize their fixed points and prove that the induced greedy stationary policy is optimal for the exponential-utility objective among stationary policies. These structural results lead to two model-free algorithms: a two-timescale Q-learning--style algorithm, for which we establish almost-sure convergence and provide finite-time convergence rates via timescale separation, and a one-timescale algorithm governed by a sublinear power-law operator. Since the latter does not admit a global contraction in standard metrics, we prove its convergence using delicate arguments based on local Lipschitzness, monotonicity, homogeneity, and Dini derivatives, and provide a scalar finite-time analysis that highlights the challenges in obtaining convergence rates in the vector case. Our work provides a foundation for value-based RL under exponential-utility objectives.

We present the first theoretical guarantees for differentially private online reinforcement learning (RL) with general function approximation, extending beyond prior work restricted to tabular and linear settings. Our approach combines a batched policy update scheme with the exponential mechanism, together with a novel regret analysis. We show that, even under general function approximation, the regret in the model-free setting under differential privacy matches the state of the art for the linear case, scaling as $\widetilde{O}(K^{3/5})$, where $K$ denotes the number of episodes. As an important by-product, we also establish the first regret bound for online RL with batch update that depends on the standard complexity measure of coverability, complementing existing results based on a newly introduced Eluder-Condition class. In addition, we uncover fundamental gaps in recent results for private RL with linear function approximation, thereby clarifying its landscape.

Recent research has revived and amplified interest in algorithms for undiscounted average reward reinforcement learning in infinite-horizon, non-episodic (continuing) tasks. Semi-Markov decision processes (SMDPs) are of particular interest. In SMDPs, discrete actions stochastically generate both rewards and durations, and the objective is to optimize the average reward rate. Existing algorithms approach this by optimizing the ratio of rewards to durations. However, when rewards and durations are non-stationary (in the infinite horizon), this can be incorrect. This paper presents a novel modified harmonic mean operator that correctly computes reward rates even under such conditions. This yields model-free learning algorithms that can work with SMDPs, while maintaining robustness to non-stationary reward and duration distributions over time. We prove theoretical properties of the modified harmonic mean operator, and empirically demonstrate its efficacy in comparison to existing algorithms.

We study model-free reinforcement learning (RL) in non-stationary finite-horizon episodic Markov decision processes (MDPs) without prior knowledge of the non-stationarity. We focus on the piecewise stationary (PS) setting, where both rewards and transition dynamics can change at unknown times. We first revisit existing state-of-the-art approaches and identify theoretical and practical limitations that change the current landscape of performance guarantees. To characterize the difficulty of the problem, we establish the first minimax lower bounds for PS-RL in tabular and linear MDPs. We then introduce Detection Augmented Reinforcement Learning (DARLING), a modular wrapper for PS-RL that applies to both tabular and linear MDPs, without knowledge of the changes. In tabular MDPs, under change-point separability and reachability conditions, DARLING improves the best known dynamic regret bounds and matches our minimax lower bound. In linear MDPs, DARLING matches the minimax lower bound when the relevant reachability parameters are known, and our analysis clarifies the structural obstacles that distinguish this setting from the tabular case. Finally, through extensive experimentation across diverse non-stationary benchmarks, we show that DARLING consistently surpasses the state-of-the-art methods.

In general reinforcement learning, all established optimal agents, including AIXI, are model-based, explicitly maintaining and using environment models. This paper introduces Universal AI with Q-Induction (AIQI), the first model-free agent proven to be asymptotically $\varepsilon$-optimal in general RL. AIQI performs universal induction over distributional action-value functions, instead of policies or environments like previous works. Under a grain of truth condition, we prove that AIQI is strong asymptotically $\varepsilon$-optimal and asymptotically $\varepsilon$-Bayes-optimal. We also apply our novel proof techniques to show asymptotic $\varepsilon$-optimality of Self-AIXI without any ad-hoc assumptions. Our results significantly expand the diversity of known universal agents.

How does the amount of compute available to a reinforcement learning (RL) policy affect its learning? Can policies using a fixed amount of parameters, still benefit from additional compute? The standard RL framework does not provide a language to answer these questions formally. Empirically, deep RL policies are often parameterized as neural networks with static architectures, conflating the amount of compute and the number of parameters. In this paper, we formalize compute bounded policies and prove that policies which use more compute can solve problems and generalize to longer-horizon tasks that are outside the scope of policies with less compute. Building on prior work in algorithmic learning and model-free planning, we propose a minimal architecture that can use a variable amount of compute. Our experiments complement our theory. On a set 31 different tasks spanning online and offline RL, we show that $(1)$ this architecture achieves stronger performance simply by using more compute, and $(2)$ stronger generalization on longer-horizon test tasks compared to standard feedforward networks or deep residual network using up to 5 times more parameters.

Stabilizing a dynamical system is a fundamental problem that serves as a cornerstone for many complex tasks in the field of control systems. The problem becomes challenging when the system model is unknown. Among the Reinforcement Learning (RL) algorithms that have been successfully applied to solve problems pertaining to unknown linear dynamical systems, the policy gradient (PG) method stands out due to its ease of implementation and can solve the problem in a model-free manner. However, most of the existing works on PG methods for unknown linear dynamical systems assume full-state feedback. In this paper, we take a step towards model-free learning for partially observed linear dynamical systems with output feedback and focus on the fundamental stabilization problem of the system. We propose an algorithmic framework that stretches the boundary of PG methods to the problem without global convergence guarantees. We show that by leveraging zeroth-order PG update based on system trajectories and its convergence to stationary points, the proposed algorithms return a stabilizing output feedback policy for discrete-time linear dynamical systems. We also explicitly characterize the sample complexity of our algorithm and verify the effectiveness of the algorithm using numerical examples.

Multi-agent games in dynamic nonlinear settings are challenging due to the time-varying interactions among the agents and the non-stationarity of the (potential) Nash equilibria. In this paper we consider model-free games, where agent transitions and costs are observed without knowledge of the transition and cost functions that generate them. We propose a novel distributed policy structure that follows the communication constraints in multi-team games, with multiple agents per team, and learned through policy gradients. Our formulation is inspired by the structure of distributed policies in linear quadratic games, which take the form of time-varying linear feedback gains. In the nonlinear case, we model the policies as nonlinear feedback gains, parameterized by self-attention layers to account for the time-varying multi-agent communication topology. We demonstrate that our approach achieves strong performance in several settings, including distributed linear and nonlinear regulation, and simulated and real multi-robot pursuit-and-evasion games.

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.

Robust reinforcement learning (RL) under the average-reward criterion is essential for long-term decision-making, particularly when the environment may differ from its training dynamics. However, most existing studies focus on model-based settings and provide only asymptotic guarantees, hindering their principled understanding and practical deployment, especially in data-limited scenarios. We aim to close this gap by proposing a model-free algorithm, \textbf{Robust Halpern Iteration (RHI)}. We first design our algorithm based on a black-box sampling oracle, which can estimate the worst-case performance accurately. We then derive the finite sample complexity of RHI under the generative model setting, assuming the sampling oracle. To concretely design such an oracle, we propose a $K$-order multi-level Monte-Carlo estimator, which is shown to have a lower bias compared to prior methods. We further instantiate our design for multiple uncertainty models, including KL and $χ^2$ divergence sets, and show that our RHI algorithm achieves an $\varepsilon$-optimal robust policy with a sample complexity of $\tilde{\mathcal{O}}\left( \frac{SA\mathcal{H}^2}{\varepsilon^{(2+o(1))}}\right)$, where $S,A$ are the number of states and actions, and $\mathcal{H}$ is the robust optimal span. Our result asymptotically matches the best complexity in robust average reward RL.

Imperfect Information Games (IIGs) are used to model games under uncertainty or lack complete information. Counterfactual Regret Minimization (CFR) is one of the most successful families of algorithms for IIGs. The integration of skill-based strategy learning with CFR could potentially mirror more human-like decision-making and improve learning on complex IIGs. It enables the learning of a hierarchical strategy, wherein low-level components represent skills for solving subgames and the high-level component manages the transition between skills. In this paper, we introduce the first hierarchical version of Deep CFR (HDCFR), an innovative method that boosts learning efficiency in tasks involving extensively large state spaces and deep game trees. Notably, HDCFR enables learning with predefined (human) expertise and extracting skills transferable to similar tasks. We first present the algorithm and establish its theory in a tabular setting, including hierarchical CFR update rules and a variance-reduced Monte Carlo sampling extension for the model-free setting, where backtracking is infeasible. We then extend HDCFR to large-scale tasks via deep learning objectives that match the tabular targets under exact function fitting. Code: https://anonymous.4open.science/r/HDCFR_RUN-677B.

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%.