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Bandit Convex Optimization in Non-stationary Environments (1907.12340v2)

Published 29 Jul 2019 in cs.LG and stat.ML

Abstract: Bandit Convex Optimization (BCO) is a fundamental framework for modeling sequential decision-making with partial information, where the only feedback available to the player is the one-point or two-point function values. In this paper, we investigate BCO in non-stationary environments and choose the \emph{dynamic regret} as the performance measure, which is defined as the difference between the cumulative loss incurred by the algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length of the comparator sequence that reflects the non-stationarity of environments. We propose a novel algorithm that achieves $O(T{3/4}(1+P_T){1/2})$ and $O(T{1/2}(1+P_T){1/2})$ dynamic regret respectively for the one-point and two-point feedback models. The latter result is optimal, matching the $\Omega(T{1/2}(1+P_T){1/2})$ lower bound established in this paper. Notably, our algorithm is more adaptive to non-stationary environments since it does not require prior knowledge of the path-length $P_T$ ahead of time, which is generally unknown.

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