no code implementations • 18 Oct 2023 • Nataša Bolić, Tommaso Cesari, Roberto Colomboni
If the distribution admits a density bounded by some constant $M$, then, for any time horizon $T$: $\bullet$ If the agents' valuations are revealed after each interaction, we provide an algorithm achieving regret $M \log T$ and show this rate is optimal, up to constant factors.
no code implementations • 14 Oct 2023 • Nicolo Cesa-Bianchi, Roberto Colomboni, Maximilian Kasy
This implies that (i) welfare maximization is harder than the multi-armed bandit problem (with a rate of $T^{1/2}$ for finite policy sets), and (ii) our algorithm achieves the optimal rate.
no code implementations • 14 Jul 2023 • Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi
We study the problem of regret minimization for a single bidder in a sequence of first-price auctions where the bidder discovers the item's value only if the auction is won.
no code implementations • 13 Jul 2023 • Roberto Colomboni, Emmanuel Esposito, Andrea Paudice
The fat-shattering dimension characterizes the uniform convergence property of real-valued functions.
no code implementations • 21 Feb 2023 • Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi
We provide a complete characterization of the regret regimes for fixed-price mechanisms under different feedback models in the two cases where the learner can post either the same or different prices to buyers and sellers.
no code implementations • 2 Sep 2022 • François Bachoc, Tommaso Cesari, Roberto Colomboni, Andrea Paudice
We analyze the cumulative regret of the Dyadic Search algorithm of Bachoc et al. [2022].
no code implementations • 13 Aug 2022 • François Bachoc, Tommaso Cesari, Roberto Colomboni, Andrea Paudice
This paper studies a natural generalization of the problem of minimizing a univariate convex function $f$ by querying its values sequentially.
no code implementations • 6 Dec 2021 • Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Claudio Gentile, Yishay Mansour
We investigate a nonstochastic bandit setting in which the loss of an action is not immediately charged to the player, but rather spread over the subsequent rounds in an adversarial way.
no code implementations • 8 Sep 2021 • Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi
In this paper, we cast the bilateral trade problem in a regret minimization framework over $T$ rounds of seller/buyer interactions, with no prior knowledge on their private valuations.
no code implementations • 16 Feb 2021 • Nicolò Cesa-Bianchi, Tommaso Cesari, Roberto Colomboni, Federico Fusco, Stefano Leonardi
Despite the simplicity of this problem, a classical result by Myerson and Satterthwaite (1983) affirms the impossibility of designing a mechanism which is simultaneously efficient, incentive compatible, individually rational, and budget balanced.
no code implementations • 8 Jul 2020 • Tommaso Cesari, Roberto Colomboni
The property of almost every point being a Lebesgue point has proven to be crucial for the consistency of several classification algorithms based on nearest neighbors.