Avik Kar

Avik Kar, Rahul Singh

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.

Rahul Singh, Akshay Mete, Avik Kar et al.

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.