An Adaptive Algorithm for Finite Stochastic Partial Monitoring

TL;DR

This paper introduces an adaptive anytime algorithm for finite stochastic partial monitoring that achieves near-optimal regret across various problem complexities, including easy and hard instances, with specific benefits in dynamic pricing scenarios.

Contribution

The paper proposes a novel adaptive algorithm that attains near-optimal regret in finite stochastic partial monitoring, adapting to problem difficulty and opponent strategies.

Findings

Achieves minimax regret within logarithmic factors for all problem types.

Attains logarithmic individual regret for easy problems.

Demonstrates O(√T) regret in dynamic pricing under certain conditions.

Abstract

We present a new anytime algorithm that achieves near-optimal regret for any instance of finite stochastic partial monitoring. In particular, the new algorithm achieves the minimax regret, within logarithmic factors, for both "easy" and "hard" problems. For easy problems, it additionally achieves logarithmic individual regret. Most importantly, the algorithm is adaptive in the sense that if the opponent strategy is in an "easy region" of the strategy space then the regret grows as if the problem was easy. As an implication, we show that under some reasonable additional assumptions, the algorithm enjoys an O(\sqrt{T}) regret in Dynamic Pricing, proven to be hard by Bartok et al. (2011).