We show with confidence bound based bidding, and'Average Pricing' there

We investigate the problem of maximizing social welfare while ensuring fairness in a multi-agent multi-armed bandit (MA-MAB) setting. In this problem, a centralized decision-maker takes actions over time, generating random rewards for various agents. Our goal is to maximize the sum of expected cumulative rewards, a.k.a. social welfare, while ensuring that each agent receives an expected reward that is at least a constant fraction of the maximum possible expected reward. Our proposed algorithm, RewardFairUCB, leverages the Upper Confidence Bound (UCB) technique to achieve sublinear regret bounds for both fairness and social welfare. The fairness regret measures the positive difference between the minimum reward guarantee and the expected reward of a given policy, whereas the social welfare regret measures the difference between the social welfare of the optimal fair policy and that of the given policy. We show that RewardFairUCB algorithm achieves instance-independent social welfare regret guarantees of $\tilde{O}(T^{1/2})$ and a fairness regret upper bound of $\tilde{O}(T^{3/4})$. We also give the lower bound of $\Omega(\sqrt{T})$ for both social welfare and fairness regret. We evaluate RewardFairUCB's performance against various baseline and heuristic algorithms using simulated data and real world data, highlighting trade-offs between fairness and social welfare regrets.

Large-scale online recommendation systems must facilitate the allocation of a limited number of items among competing users while learning their preferences from user feedback. As a principled way of incorporating market constraints and user incentives in the design, we consider our objectives to be two-fold: maximal social welfare with minimal instability. To maximize social welfare, our proposed framework enhances the quality of recommendations by exploring allocations that optimistically maximize the rewards. To minimize instability, a measure of users' incentives to deviate from recommended allocations, the algorithm prices the items based on a scheme derived from the Walrasian equilibria. Though it is known that these equilibria yield stable prices for markets with known user preferences, our approach accounts for the inherent uncertainty in the preferences and further ensures that the users accept their recommendations under offered prices. To the best of our knowledge, our approach is the first to integrate techniques from combinatorial bandits, optimal resource allocation, and collaborative filtering to obtain an algorithm that achieves sub-linear social welfare regret as well as sub-linear instability. Empirical studies on synthetic and real-world data also demonstrate the efficacy of our strategy compared to approaches that do not fully incorporate all these aspects.