arXiv subjects

Avik Kar

Publications and source records attributed to Avik Kar.

5 recordsLinked to original sources

arXiv2026

Policy Gradient Methods for Non-Markovian Reinforcement Learning

We study policy gradient methods for reinforcement learning in non-Markovian decision processes (NMDPs), where observations and rewards depend on the entire interaction history. To handle this dependence, the agent maintains an internal state that is recursively updated to provide a compact summary of past observations and actions. In contrast to approaches that treat the agent state dynamics as fixed or learn it via predictive objectives, we propose a reward-centric formulation that jointly optimizes the agent state dynamics and the control policy to maximize the expected cumulative reward. To this end, we consider a class of Agent State-Markov (ASM) policies, comprising an agent state dynamics and a control policy that maps the agent state to actions. We establish a novel policy gradient theorem for ASM policies, extending the classical policy gradient results from the Markovian setting to episodic and infinite-horizon discounted NMDPs. Building on this gradient expression, we propose the Agent State-Markov Policy Gradient (ASMPG) algorithm, which leverages the recursive structure of the agent state dynamics for efficient optimization. We establish finite-time and almost sure convergence guarantees, and empirically demonstrate that, on a range of non-Markovian tasks, ASMPG outperforms baselines that learn state representations via predictive objectives.

cs.LG↗

arXiv2026

High-Probability Bounds for SGD under the Polyak-Lojasiewicz Condition with Markovian Noise

We present the first uniform-in-time high-probability bound for SGD under the PL condition, where the gradient noise contains both Markovian and martingale difference components. This significantly broadens the scope of finite-time guarantees, as the PL condition arises in many machine learning and deep learning models while Markovian noise naturally arises in decentralized optimization and online system identification problems. We further allow the magnitude of noise to grow with the function value, enabling the analysis of many practical sampling strategies. In addition to the high-probability guarantee, we establish a matching $1/k$ decay rate for the expected suboptimality. Our proof technique relies on the Poisson equation to handle the Markovian noise and a probabilistic induction argument to address the lack of almost-sure bounds on the objective. Finally, we demonstrate the applicability of our framework by analyzing three practical optimization problems: token-based decentralized linear regression, supervised learning with subsampling for privacy amplification, and online system identification.

cs.LG↗

arXiv2024

Provably Adaptive Average Reward Reinforcement Learning for Metric Spaces

We study infinite-horizon average-reward reinforcement learning (RL) for Lipschitz MDPs, a broad class that subsumes several important classes such as linear and RKHS MDPs, function approximation frameworks, and develop an adaptive algorithm $\text{ZoRL}$ with regret bounded as $\mathcal{O}\big(T^{1 - d_{\text{eff.}}^{-1}}\big)$, where $d_{\text{eff.}}= 2d_\mathcal{S} + d_z + 3$, $d_\mathcal{S}$ is the dimension of the state space and $d_z$ is the zooming dimension. In contrast, algorithms with fixed discretization yield $d_{\text{eff.}} = 2(d_\mathcal{S} + d_\mathcal{A}) + 2$, $d_\mathcal{A}$ being the dimension of action space. $\text{ZoRL}$ achieves this by discretizing the state-action space adaptively and zooming into ''promising regions'' of the state-action space. $d_z$, a problem-dependent quantity bounded by the state-action space's dimension, allows us to conclude that if an MDP is benign, then the regret of $\text{ZoRL}$ will be small. The zooming dimension and $\text{ZoRL}$ are truly adaptive, i.e., the current work shows how to capture adaptivity gains for infinite-horizon average-reward RL. $\text{ZoRL}$ outperforms other state-of-the-art algorithms in experiments, thereby demonstrating the gains arising due to adaptivity.

cs.LG↗

arXiv2024

Policy Zooming: Adaptive Discretization-based Infinite-Horizon Average-Reward Reinforcement Learning

We study the infinite-horizon average-reward reinforcement learning (RL) for continuous space Lipschitz MDPs in which an agent can play policies from a given set $\Phi$. The proposed algorithms efficiently explore the policy space by ''zooming'' into the ''promising regions'' of $\Phi$, thereby achieving adaptivity gains in the performance. We upper bound their regret as $\tilde{\mathcal{O}}\big(T^{1 - d_{\text{eff.}}^{-1}}\big)$, where $d_{\text{eff.}} = d^\Phi_z+2$ for model-free algoritahm $\textit{PZRL-MF}$ and $d_{\text{eff.}} = 2d_\mathcal{S} + d^\Phi_z + 3$ for model-based algorithm $\textit{PZRL-MB}$. Here, $d_\mathcal{S}$ is the dimension of the state space, and $d^\Phi_z$ is the zooming dimension given a set of policies $\Phi$. $d^\Phi_z$ is an alternative measure of the complexity of the problem, and it depends on the underlying MDP as well as on $\Phi$. Hence, the proposed algorithms exhibit low regret in case the problem instance is benign and/or the agent competes against a low-complexity $\Phi$ (that has a small $d^\Phi_z$). When specialized to the case of finite-dimensional policy space, we obtain that $d_{\text{eff.}}$ scales as the dimension of this space under mild technical conditions; and also obtain $d_{\text{eff.}} = 2$, or equivalently $\tilde{\mathcal{O}}(\sqrt{T})$ regret for $\textit{PZRL-MF}$, under a curvature condition on the average reward function that is commonly used in the multi-armed bandit (MAB) literature.

cs.LG↗

arXiv2023

Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputs

Minimum variance controllers have been employed in a wide-range of industrial applications. A key challenge experienced by many adaptive controllers is their poor empirical performance in the initial stages of learning. In this paper, we address the problem of initializing them so that they provide acceptable transients, and also provide an accompanying finite-time regret analysis, for adaptive minimum variance control of an auto-regressive system with exogenous inputs (ARX). Following [3], we consider a modified version of the Certainty Equivalence (CE) adaptive controller, which we call PIECE, that utilizes probing inputs for exploration. We show that it has a $C \log T$ bound on the regret after $T$ time-steps for bounded noise, and $C\log^2 T$ in the case of sub-Gaussian noise. The simulation results demonstrate the advantage of PIECE over the algorithm proposed in [3] as well as the standard Certainty Equivalence controller especially in the initial learning phase. To the best of our knowledge, this is the first work that provides finite-time regret bounds for an adaptive minimum variance controller.

eess.SY↗