Harshat Kumar

Harshat Kumar, Dionysios S. Kalogerias, George J. Pappas et al.

Deterministic Policy Gradient (DPG) removes a level of randomness from standard randomized-action Policy Gradient (PG), and demonstrates substantial empirical success for tackling complex dynamic problems involving Markov decision processes. At the same time, though, DPG loses its ability to learn in a model-free (i.e., actor-only) fashion, frequently necessitating the use of critics in order to obtain consistent estimates of the associated policy-reward gradient. In this work, we introduce Zeroth-order Deterministic Policy Gradient (ZDPG), which approximates policy-reward gradients via two-point stochastic evaluations of the $Q$-function, constructed by properly designed low-dimensional action-space perturbations. Exploiting the idea of random horizon rollouts for obtaining unbiased estimates of the $Q$-function, ZDPG lifts the dependence on critics and restores true model-free policy learning, while enjoying built-in and provable algorithmic stability. Additionally, we present new finite sample complexity bounds for ZDPG, which improve upon existing results by up to two orders of magnitude. Our findings are supported by several numerical experiments, which showcase the effectiveness of ZDPG in a practical setting, and its advantages over both PG and Baseline PG.

Harshat Kumar, Alec Koppel, Alejandro Ribeiro

Reinforcement learning, mathematically described by Markov Decision Problems, may be approached either through dynamic programming or policy search. Actor-critic algorithms combine the merits of both approaches by alternating between steps to estimate the value function and policy gradient updates. Due to the fact that the updates exhibit correlated noise and biased gradient updates, only the asymptotic behavior of actor-critic is known by connecting its behavior to dynamical systems. This work puts forth a new variant of actor-critic that employs Monte Carlo rollouts during the policy search updates, which results in controllable bias that depends on the number of critic evaluations. As a result, we are able to provide for the first time the convergence rate of actor-critic algorithms when the policy search step employs policy gradient, agnostic to the choice of policy evaluation technique. In particular, we establish conditions under which the sample complexity is comparable to stochastic gradient method for non-convex problems or slower as a result of the critic estimation error, which is the main complexity bottleneck. These results hold in continuous state and action spaces with linear function approximation for the value function. We then specialize these conceptual results to the case where the critic is estimated by Temporal Difference, Gradient Temporal Difference, and Accelerated Gradient Temporal Difference. These learning rates are then corroborated on a navigation problem involving an obstacle and the pendulum problem which provide insight into the interplay between optimization and generalization in reinforcement learning.