Conservative Bandits
This work addresses a practical constraint for companies in dynamic decision-making, though it is incremental as it builds on prior work with weaker time constraints.
The paper tackles the problem of multi-armed bandits where a company must explore new revenue-maximizing strategies while keeping revenue above a fixed baseline at all times, addressing both stochastic and adversarial settings. It proposes novel strategies, analyzes the cost of constraints, provides regret bounds, and includes empirical validation.
We study a novel multi-armed bandit problem that models the challenge faced by a company wishing to explore new strategies to maximize revenue whilst simultaneously maintaining their revenue above a fixed baseline, uniformly over time. While previous work addressed the problem under the weaker requirement of maintaining the revenue constraint only at a given fixed time in the future, the algorithms previously proposed are unsuitable due to their design under the more stringent constraints. We consider both the stochastic and the adversarial settings, where we propose, natural, yet novel strategies and analyze the price for maintaining the constraints. Amongst other things, we prove both high probability and expectation bounds on the regret, while we also consider both the problem of maintaining the constraints with high probability or expectation. For the adversarial setting the price of maintaining the constraint appears to be higher, at least for the algorithm considered. A lower bound is given showing that the algorithm for the stochastic setting is almost optimal. Empirical results obtained in synthetic environments complement our theoretical findings.