arXiv subjects

Aviv Rosenberg

Publications and source records attributed to Aviv Rosenberg.

23 records · Page 2Linked to original sources

arXiv2021

Minimax Regret for Stochastic Shortest Path

We study the Stochastic Shortest Path (SSP) problem in which an agent has to reach a goal state in minimum total expected cost. In the learning formulation of the problem, the agent has no prior knowledge about the costs and dynamics of the model. She repeatedly interacts with the model for $K$ episodes, and has to minimize her regret. In this work we show that the minimax regret for this setting is $\widetilde O(\sqrt{ (B_\star^2 + B_\star) |S| |A| K})$ where $B_\star$ is a bound on the expected cost of the optimal policy from any state, $S$ is the state space, and $A$ is the action space. This matches the $Ω(\sqrt{ B_\star^2 |S| |A| K})$ lower bound of Rosenberg et al. [2020] for $B_\star \ge 1$, and improves their regret bound by a factor of $\sqrt{|S|}$. For $B_\star < 1$ we prove a matching lower bound of $Ω(\sqrt{ B_\star |S| |A| K})$. Our algorithm is based on a novel reduction from SSP to finite-horizon MDPs. To that end, we provide an algorithm for the finite-horizon setting whose leading term in the regret depends polynomially on the expected cost of the optimal policy and only logarithmically on the horizon.

cs.LG↗

arXiv2021

Oracle-Efficient Regret Minimization in Factored MDPs with Unknown Structure

We study regret minimization in non-episodic factored Markov decision processes (FMDPs), where all existing algorithms make the strong assumption that the factored structure of the FMDP is known to the learner in advance. In this paper, we provide the first algorithm that learns the structure of the FMDP while minimizing the regret. Our algorithm is based on the optimism in face of uncertainty principle, combined with a simple statistical method for structure learning, and can be implemented efficiently given oracle-access to an FMDP planner. Moreover, we give a variant of our algorithm that remains efficient even when the oracle is limited to non-factored actions, which is the case with almost all existing approximate planners. Finally, we leverage our techniques to prove a novel lower bound for the known structure case, closing the gap to the regret bound of Chen et al. [2021].

cs.LG↗

arXiv2020

Optimistic Policy Optimization with Bandit Feedback

Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms. Yet, so far, such methods have been mostly analyzed from an optimization perspective, without addressing the problem of exploration, or by making strong assumptions on the interaction with the environment. In this paper we consider model-based RL in the tabular finite-horizon MDP setting with unknown transitions and bandit feedback. For this setting, we propose an optimistic trust region policy optimization (TRPO) algorithm for which we establish $\tilde O(\sqrt{S^2 A H^4 K})$ regret for stochastic rewards. Furthermore, we prove $\tilde O( \sqrt{ S^2 A H^4 } K^{2/3} ) $ regret for adversarial rewards. Interestingly, this result matches previous bounds derived for the bandit feedback case, yet with known transitions. To the best of our knowledge, the two results are the first sub-linear regret bounds obtained for policy optimization algorithms with unknown transitions and bandit feedback.

cs.LG↗

arXiv2020

Near-optimal Regret Bounds for Stochastic Shortest Path

Stochastic shortest path (SSP) is a well-known problem in planning and control, in which an agent has to reach a goal state in minimum total expected cost. In the learning formulation of the problem, the agent is unaware of the environment dynamics (i.e., the transition function) and has to repeatedly play for a given number of episodes while reasoning about the problem's optimal solution. Unlike other well-studied models in reinforcement learning (RL), the length of an episode is not predetermined (or bounded) and is influenced by the agent's actions. Recently, Tarbouriech et al. (2019) studied this problem in the context of regret minimization and provided an algorithm whose regret bound is inversely proportional to the square root of the minimum instantaneous cost. In this work we remove this dependence on the minimum cost---we give an algorithm that guarantees a regret bound of $\widetilde{O}(B_\star |S| \sqrt{|A| K})$, where $B_\star$ is an upper bound on the expected cost of the optimal policy, $S$ is the set of states, $A$ is the set of actions and $K$ is the number of episodes. We additionally show that any learning algorithm must have at least $Ω(B_\star \sqrt{|S| |A| K})$ regret in the worst case.

cs.LG↗

arXiv2019

Online Convex Optimization in Adversarial Markov Decision Processes

We consider online learning in episodic loop-free Markov decision processes (MDPs), where the loss function can change arbitrarily between episodes, and the transition function is not known to the learner. We show $\tilde{O}(L|X|\sqrt{|A|T})$ regret bound, where $T$ is the number of episodes, $X$ is the state space, $A$ is the action space, and $L$ is the length of each episode. Our online algorithm is implemented using entropic regularization methodology, which allows to extend the original adversarial MDP model to handle convex performance criteria (different ways to aggregate the losses of a single episode) , as well as improve previous regret bounds.

cs.LG↗