Ahmed Ben Yahmed

Ahmed Ben Yahmed, Clément Calauzènes, Vianney Perchet · pku

In the strategic multi-armed bandit setting, when arms possess perfect information about the player's behavior, they can establish an equilibrium where: 1. they retain almost all of their value, 2. they leave the player with a substantial (linear) regret. This study illustrates that, even if complete information is not publicly available to all arms but is shared among them, it is possible to achieve a similar equilibrium. The primary challenge lies in designing a communication protocol that incentivizes the arms to communicate truthfully.

Alexandre Gilotte, Ahmed Ben Yahmed, David Rohde

Aggregating a dataset, then injecting some noise, is a simple and common way to release differentially private data.However, aggregated data -- even without noise -- is not an appropriate input for machine learning classifiers.In this work, we show how a new model, similar to a logistic regression, may be learned from aggregated data only by approximating the unobserved feature distribution with a maximum entropy hypothesis. The resulting model is a Markov Random Field (MRF), and we detail how to apply, modify and scale a MRF training algorithm to our setting. Finally we present empirical evidence on several public datasets that the model learned this way can achieve performances comparable to those of a logistic model trained with the full unaggregated data.

Ahmed Ben Yahmed, Clément Calauzènes, Vianney Perchet

We consider the classical multi-armed bandit problem, but with strategic arms. In this context, each arm is characterized by a bounded support reward distribution and strategically aims to maximize its own utility by potentially retaining a portion of its reward, and disclosing only a fraction of it to the learning agent. This scenario unfolds as a game over $T$ rounds, leading to a competition of objectives between the learning agent, aiming to minimize their regret, and the arms, motivated by the desire to maximize their individual utilities. To address these dynamics, we introduce a new mechanism that establishes an equilibrium wherein each arm behaves truthfully and discloses as much of its rewards as possible. With this mechanism, the agent can attain the second-highest average (true) reward among arms, with a cumulative regret bounded by $O(\log(T)/Δ)$ (problem-dependent) or $O(\sqrt{T\log(T)})$ (worst-case).

Ahmed Ben Yahmed, Hafedh El Ferchichi, Marc Abeille et al.

We examine a multi-armed bandit problem with contextual information, where the objective is to ensure that each arm receives a minimum aggregated reward across contexts while simultaneously maximizing the total cumulative reward. This framework captures a broad class of real-world applications where fair revenue allocation is critical and contextual variation is inherent. The cross-context aggregation of minimum reward constraints, while enabling better performance and easier feasibility, introduces significant technical challenges -- particularly the absence of closed-form optimal allocations typically available in standard MAB settings. We design and analyze algorithms that either optimistically prioritize performance or pessimistically enforce constraint satisfaction. For each algorithm, we derive problem-dependent upper bounds on both regret and constraint violations. Furthermore, we establish a lower bound demonstrating that the dependence on the time horizon in our results is optimal in general and revealing fundamental limitations of the free exploration principle leveraged in prior work.