Accelerating Value Iteration with Anchoring Jongmin Lee 1 Ernest K. Ryu Department of Mathematical Science, Seoul National University

Surprisingly, however, the optimal rate in terms of Bellman error for the VI setup was not known, and finding a general acceleration mechanism has been an open problem. In this paper, we present the first accelerated VI for both the Bellman consistency and optimality operators. Our method, called Anc-VI, is based on an anchoring mechanism (distinct from Nesterov's acceleration), and it reduces the Bellman error faster than standard VI. In particular, Anc-VI exhibits a O(1/k)-rate for γ 1 or even γ = 1, while standard VI has rate O(1) for γ 1 1/k, where k is the iteration count. We also provide a complexity lower bound matching the upper bound up to a constant factor of 4, thereby establishing optimality of the accelerated rate of Anc-VI. Finally, we show that the anchoring mechanism provides the same benefit in the approximate VI and Gauss-Seidel VI setups as well.