arXiv subjects

Matteo Bollini

Publications and source records attributed to Matteo Bollini.

5 recordsLinked to original sources

arXiv2026

Replicable Constrained Bandits

Algorithmic \emph{replicability} has recently been introduced to address the need for reproducible experiments in machine learning. A \emph{replicable online learning} algorithm is one that takes the same sequence of decisions across different executions in the same environment, with high probability. We initiate the study of algorithmic replicability in \emph{constrained} MAB problems, where a learner interacts with an unknown stochastic environment for $T$ rounds, seeking not only to maximize reward but also to satisfy multiple constraints. Our main result is that replicability can be achieved in constrained MABs. Specifically, we design replicable algorithms whose regret and constraint violation match those of non-replicable ones in terms of $T$. As a key step toward these guarantees, we develop the first replicable UCB-like algorithm for \emph{unconstrained} MABs, showing that algorithms that employ the optimism in-the-face-of-uncertainty principle can be replicable, a result that we believe is of independent interest.

cs.LG↗

arXiv2026

Learning in Bayesian Stackelberg Games With Unknown Follower's Types

We study online learning in Bayesian Stackelberg games, where a leader repeatedly interacts with a follower whose unknown private type is independently drawn at each round from an unknown probability distribution. The goal is to design algorithms that minimize the leader's regret with respect to always playing an optimal commitment computed with knowledge of the game. We consider, for the first time to the best of our knowledge, the most realistic case in which the leader does not know anything about the follower's types, i.e., the possible follower payoffs. This raises considerable additional challenges compared to the commonly studied case in which the payoffs of follower types are known. First, we prove a strong negative result: no-regret is unattainable under action feedback, i.e., when the leader only observes the follower's best response at the end of each round. Thus, we focus on the easier type feedback model, where the follower's type is also revealed. In such a setting, we propose a no-regret algorithm that achieves a regret of $\widetilde{O}(\sqrt{T})$, when ignoring the dependence on other parameters.

cs.GT↗

arXiv2024

Online Bayesian Persuasion Without a Clue

We study online Bayesian persuasion problems in which an informed sender repeatedly faces a receiver with the goal of influencing their behavior through the provision of payoff-relevant information. Previous works assume that the sender has knowledge about either the prior distribution over states of nature or receiver's utilities, or both. We relax such unrealistic assumptions by considering settings in which the sender does not know anything about the prior and the receiver. We design an algorithm that achieves sublinear regret with respect to an optimal signaling scheme, and we also provide a collection of lower bounds showing that the guarantees of such an algorithm are tight. Our algorithm works by searching a suitable space of signaling schemes in order to learn receiver's best responses. To do this, we leverage a non-standard representation of signaling schemes that allows to cleverly overcome the challenge of not knowing anything about the prior over states of nature and receiver's utilities. Finally, our results also allow to derive lower/upper bounds on the sample complexity of learning signaling schemes in a related Bayesian persuasion PAC-learning problem.

cs.GT↗

arXiv2024

Contracting With a Reinforcement Learning Agent by Playing Trick or Treat

We study principal-agent problems where a farsighted agent takes costly actions in an MDP. The core challenge in these settings is that agent's actions are hidden to the principal, who can only observe their outcomes, namely state transitions and their associated rewards. Thus, the principal's goal is to devise a policy that incentives the agent to take actions leading to desirable outcomes. This is accomplished by committing to a payment scheme (a.k.a. contract) at each step, specifying a monetary transfer from the principal to the agent for every possible outcome. Interestingly, we show that Markovian policies are unfit in these settings, as they do not allow to achieve the optimal principal's utility and are constitutionally intractable. Thus, accounting for history in unavoidable, and this begets considerable additional challenges compared to standard MDPs. Nevertheless, we design an efficient algorithm to compute an optimal policy, leveraging a compact way of representing histories for this purpose. Unfortunately, the policy produced by such an algorithm cannot be readily implemented, as it is only approximately incentive compatible, meaning that the agent is incentivized to take the desired actions only approximately. To fix this, we design an efficient method to make such a policy incentive compatible, by only introducing a negligible loss in principal's utility. This method can be generally applied to any approximately-incentive-compatible policy, and it generalized a related approach that has already been discovered for classical principal-agent problems to more general settings in MDPs.

cs.GT↗

arXiv2024

The Sample Complexity of Stackelberg Games

Stackelberg games (SGs) constitute the most fundamental and acclaimed models of strategic interactions involving some form of commitment. Moreover, they form the basis of more elaborate models of this kind, such as, e.g., Bayesian persuasion and principal-agent problems. Addressing learning tasks in SGs and related models is crucial to operationalize them in practice, where model parameters are usually unknown. In this paper, we revise the sample complexity of learning an optimal strategy to commit to in SGs. We provide a novel algorithm that (i) does not require any of the limiting assumptions made by state-of-the-art approaches and (ii) deals with a trade-off between sample complexity and termination probability arising when leader's strategies representation has finite precision. Such a trade-off has been completely neglected by existing algorithms and, if not properly managed, it may result in them using exponentially-many samples. Our algorithm requires novel techniques, which also pave the way to addressing learning problems in other models with commitment ubiquitous in the real world.

cs.GT↗