An Adaptive Algorithm for Finite Stochastic Partial Monitoring
This work addresses the challenge of decision-making under partial feedback for researchers and practitioners in online learning, offering an incremental improvement by adapting to problem difficulty.
The paper tackles the problem of finite stochastic partial monitoring by introducing an adaptive algorithm that achieves near-optimal regret, including minimax regret for easy and hard problems and logarithmic individual regret for easy ones, with concrete results like O(√T) regret in Dynamic Pricing.
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).