arXiv subjects

Martino Bernasconi

Publications and source records attributed to Martino Bernasconi.

30 records · Page 2Linked to original sources

arXiv2024

Feature-Based Online Bilateral Trade

Bilateral trade models the problem of facilitating trades between a seller and a buyer having private valuations for the item being sold. In the online version of the problem, the learner faces a new seller and buyer at each time step, and has to post a price for each of the two parties without any knowledge of their valuations. We consider a scenario where, at each time step, before posting prices the learner observes a context vector containing information about the features of the item for sale. The valuations of both the seller and the buyer follow an unknown linear function of the context. In this setting, the learner could leverage previous transactions in an attempt to estimate private valuations. We characterize the regret regimes of different settings, taking as a baseline the best context-dependent prices in hindsight. First, in the setting in which the learner has two-bit feedback and strong budget balance constraints, we propose an algorithm with $O(\log T)$ regret. Then, we study the same set-up with noisy valuations, providing a tight $\widetilde O(T^{\frac23})$ regret upper bound. Finally, we show that loosening budget balance constraints allows the learner to operate under more restrictive feedback. Specifically, we show how to address the one-bit, global budget balance setting through a reduction from the two-bit, strong budget balance setup. This established a fundamental trade-off between the quality of the feedback and the strictness of the budget constraints.

cs.GT↗

arXiv2024

Beyond Primal-Dual Methods in Bandits with Stochastic and Adversarial Constraints

We address a generalization of the bandit with knapsacks problem, where a learner aims to maximize rewards while satisfying an arbitrary set of long-term constraints. Our goal is to design best-of-both-worlds algorithms that perform optimally under both stochastic and adversarial constraints. Previous works address this problem via primal-dual methods, and require some stringent assumptions, namely the Slater's condition, and in adversarial settings, they either assume knowledge of a lower bound on the Slater's parameter, or impose strong requirements on the primal and dual regret minimizers such as requiring weak adaptivity. We propose an alternative and more natural approach based on optimistic estimations of the constraints. Surprisingly, we show that estimating the constraints with an UCB-like approach guarantees optimal performances. Our algorithm consists of two main components: (i) a regret minimizer working on \emph{moving strategy sets} and (ii) an estimate of the feasible set as an optimistic weighted empirical mean of previous samples. The key challenge in this approach is designing adaptive weights that meet the different requirements for stochastic and adversarial constraints. Our algorithm is significantly simpler than previous approaches, and has a cleaner analysis. Moreover, ours is the first best-of-both-worlds algorithm providing bounds logarithmic in the number of constraints. Additionally, in stochastic settings, it provides $\widetilde O(\sqrt{T})$ regret \emph{without} Slater's condition.

cs.LG↗

arXiv2024

No-Regret is not enough! Bandits with General Constraints through Adaptive Regret Minimization

In the bandits with knapsacks framework (BwK) the learner has $m$ resource-consumption (packing) constraints. We focus on the generalization of BwK in which the learner has a set of general long-term constraints. The goal of the learner is to maximize their cumulative reward, while at the same time achieving small cumulative constraints violations. In this scenario, there exist simple instances where conventional methods for BwK fail to yield sublinear violations of constraints. We show that it is possible to circumvent this issue by requiring the primal and dual algorithm to be weakly adaptive. Indeed, even in absence on any information on the Slater's parameter $ρ$ characterizing the problem, the interplay between weakly adaptive primal and dual regret minimizers yields a "self-bounding" property of dual variables. In particular, their norm remains suitably upper bounded across the entire time horizon even without explicit projection steps. By exploiting this property, we provide best-of-both-worlds guarantees for stochastic and adversarial inputs. In the first case, we show that the algorithm guarantees sublinear regret. In the latter case, we establish a tight competitive ratio of $ρ/(1+ρ)$. In both settings, constraints violations are guaranteed to be sublinear in time. Finally, this results allow us to obtain new result for the problem of contextual bandits with linear constraints, providing the first no-$α$-regret guarantees for adversarial contexts.

cs.LG↗

arXiv2024

No-Regret Learning in Bilateral Trade via Global Budget Balance

Bilateral trade models the problem of intermediating between two rational agents -- a seller and a buyer -- both characterized by a private valuation for an item they want to trade. We study the online learning version of the problem, in which at each time step a new seller and buyer arrive and the learner has to set prices for them without any knowledge about their (adversarially generated) valuations. In this setting, known impossibility results rule out the existence of no-regret algorithms when budget balanced has to be enforced at each time step. In this paper, we introduce the notion of \emph{global budget balance}, which only requires the learner to fulfill budget balance over the entire time horizon. Under this natural relaxation, we provide the first no-regret algorithms for adversarial bilateral trade under various feedback models. First, we show that in the full-feedback model, the learner can guarantee $\tilde O(\sqrt{T})$ regret against the best fixed prices in hindsight, and that this bound is optimal up to poly-logarithmic terms. Second, we provide a learning algorithm guaranteeing a $\tilde O(T^{3/4})$ regret upper bound with one-bit feedback, which we complement with a $Ω(T^{5/7})$ lower bound that holds even in the two-bit feedback model. Finally, we introduce and analyze an alternative benchmark that is provably stronger than the best fixed prices in hindsight and is inspired by the literature on bandits with knapsacks.

cs.GT↗

arXiv2024

Agent-Designed Contracts: How to Sell Hidden Actions

We study the problem faced by a service provider that has to sell services to a user. In our model the service provider proposes various payment options (a menu) to the user which may be based, for example, on the quality of the service. Then, the user chooses one of these options and pays an amount to the service provider, contingent on the observed final outcome. Users are not able to observe directly the action performed by the service provide to reach the final outcome. This might incentivize misconduct. Therefore, we propose a model that enforces trust through economics incentives. The problem has two crucial features: i) the service provider is responsible for both formulating the contract and performing the action for which the user issues payments, and ii) the user is unaware of the true action carried out by the service provider, which is hidden. We study this delegation problem through the lens of contract design, with the overarching goal of enabling the computation of contracts that guarantee that the user can trust the service provider, even if their action is hidden.

cs.GT↗

arXiv2024

Regret-Minimizing Contracts: Agency Under Uncertainty

We study the fundamental problem of designing contracts in principal-agent problems under uncertainty. Previous works mostly addressed Bayesian settings in which principal's uncertainty is modeled as a probability distribution over agent's types. In this paper, we study a setting in which the principal has no distributional information about agent's type. In particular, in our setting, the principal only knows some uncertainty set defining possible agent's action costs. Thus, the principal takes a robust (adversarial) approach by trying to design contracts which minimize the (additive) regret: the maximum difference between what the principal could have obtained had them known agent's costs and what they actually get under the selected contract.

cs.GT↗

arXiv2024

Multi-Agent Contract Design beyond Binary Actions

We study hidden-action principal-agent problems with multiple agents. Unlike previous work, we consider a general setting in which each agent has an arbitrary number of actions, and the joint action induces outcomes according to an arbitrary distribution. We study two classes of mechanisms: a class of deterministic mechanisms that is the natural extension of single-agent contracts, in which the agents play a Nash equilibrium of the game induced by the contract, and a class of randomized mechanisms that is inspired by single-agent randomized contracts and correlated equilibria.

cs.GT↗

arXiv2023

Persuading Farsighted Receivers in MDPs: the Power of Honesty

Bayesian persuasion studies the problem faced by an informed sender who strategically discloses information to influence the behavior of an uninformed receiver. Recently, a growing attention has been devoted to settings where the sender and the receiver interact sequentially, in which the receiver's decision-making problem is usually modeled as a Markov decision process (MDP). However, previous works focused on computing optimal information-revelation policies (a.k.a. signaling schemes) under the restrictive assumption that the receiver acts myopically, selecting actions to maximize the one-step utility and disregarding future rewards. This is justified by the fact that, when the receiver is farsighted and thus considers future rewards, finding an optimal Markovian signaling scheme is NP-hard. In this paper, we show that Markovian signaling schemes do not constitute the "right" class of policies. Indeed, differently from most of the MDPs settings, we prove that Markovian signaling schemes are not optimal, and general history-dependent signaling schemes should be considered. Moreover, we also show that history-dependent signaling schemes circumvent the negative complexity results affecting Markovian signaling schemes. Formally, we design an algorithm that computes an optimal and ε-persuasive history-dependent signaling scheme in time polynomial in 1/ε and in the instance size. The crucial challenge is that general history-dependent signaling schemes cannot be represented in polynomial space. Nevertheless, we introduce a convenient subclass of history-dependent signaling schemes, called promise-form, which are as powerful as general history-dependent ones and efficiently representable. Intuitively, promise-form signaling schemes compactly encode histories in the form of honest promises on future receiver's rewards.

cs.GT↗

arXiv2023

Bandits with Replenishable Knapsacks: the Best of both Worlds

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio $α$ when $B=Ω(T)$ or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent $\tilde{O}(T^{1/2})$ regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

cs.LG↗

arXiv2023

Optimal Rates and Efficient Algorithms for Online Bayesian Persuasion

Bayesian persuasion studies how an informed sender should influence beliefs of rational receivers who take decisions through Bayesian updating of a common prior. We focus on the online Bayesian persuasion framework, in which the sender repeatedly faces one or more receivers with unknown and adversarially selected types. First, we show how to obtain a tight $\tilde O(T^{1/2})$ regret bound in the case in which the sender faces a single receiver and has partial feedback, improving over the best previously known bound of $\tilde O(T^{4/5})$. Then, we provide the first no-regret guarantees for the multi-receiver setting under partial feedback. Finally, we show how to design no-regret algorithms with polynomial per-iteration running time by exploiting type reporting, thereby circumventing known intractability results on online Bayesian persuasion. We provide efficient algorithms guaranteeing a $O(T^{1/2})$ regret upper bound both in the single- and multi-receiver scenario when type reporting is allowed.

cs.GT↗

arXiv2022

Sequential Information Design: Learning to Persuade in the Dark

We study a repeated information design problem faced by an informed sender who tries to influence the behavior of a self-interested receiver. We consider settings where the receiver faces a sequential decision making (SDM) problem. At each round, the sender observes the realizations of random events in the SDM problem. This begets the challenge of how to incrementally disclose such information to the receiver to persuade them to follow (desirable) action recommendations. We study the case in which the sender does not know random events probabilities, and, thus, they have to gradually learn them while persuading the receiver. We start by providing a non-trivial polytopal approximation of the set of sender's persuasive information structures. This is crucial to design efficient learning algorithms. Next, we prove a negative result: no learning algorithm can be persuasive. Thus, we relax persuasiveness requirements by focusing on algorithms that guarantee that the receiver's regret in following recommendations grows sub-linearly. In the full-feedback setting -- where the sender observes all random events realizations -- , we provide an algorithm with $\tilde{O}(\sqrt{T})$ regret for both the sender and the receiver. Instead, in the bandit-feedback setting -- where the sender only observes the realizations of random events actually occurring in the SDM problem -- , we design an algorithm that, given an $α\in [1/2, 1]$ as input, ensures $\tilde{O}({T^α})$ and $\tilde{O}( T^{\max \{ α, 1-\fracα{2} \} })$ regrets, for the sender and the receiver respectively. This result is complemented by a lower bound showing that such a regrets trade-off is essentially tight.

cs.LG↗

arXiv2022

Last-iterate Convergence to Trembling-hand Perfect Equilibria

Designing efficient algorithms to find Nash equilibrium (NE) refinements in sequential games is of paramount importance in practice. Indeed, it is well known that the NE has several weaknesses, since it may prescribe to play sub-optimal actions in those parts of the game that are never reached at the equilibrium. NE refinements, such as the extensive-form perfect equilibrium (EFPE), amend such weaknesses by accounting for the possibility of players' mistakes. This is crucial in real-world applications, where bounded rationality players are usually involved, and it turns out being useful also in boosting the performances of superhuman agents for recreational games like Poker. Nevertheless, only few works addressed the problem of computing NE refinements. Most of them propose algorithms finding exact NE refinements by means of linear programming, and, thus, these do not have the potential of scaling up to real-world-size games. On the other hand, existing iterative algorithms that exploit the tree structure of sequential games only provide convergence guarantees to approximate refinements. In this paper, we provide the first efficient last-iterate algorithm that provably converges to an EFPE in two-player zero-sum sequential games with imperfect information. Our algorithm works by tracking a sequence of equilibria of suitably-defined, regularized-perturbed games. In order to do that, it uses a procedure that is tailored to converge last-iterate to the equilibria of such games. Crucially, the updates performed by such a procedure can be performed efficiently by visiting the game tree, thus making our algorithm potentially more scalable than its linear-programming-based competitors. Finally, we evaluate our algorithm on a standard testbed of games, showing that it produces strategies which are much more robust to players' mistakes than those of state-of-the-art NE-computation algorithms.

cs.GT↗