arXiv subjects

Benoit Duvocelle

Publications and source records attributed to Benoit Duvocelle.

4 recordsLinked to original sources

arXiv2020

A competitive search game with a moving target

We introduce a discrete-time search game, in which two players compete to find an object first. The object moves according to a time-varying Markov chain on finitely many states. The players know the Markov chain and the initial probability distribution of the object, but do not observe the current state of the object. The players are active in turns. The active player chooses a state, and this choice is observed by the other player. If the object is in the chosen state, this player wins and the game ends. Otherwise, the object moves according to the Markov chain and the game continues at the next period. We show that this game admits a value, and for any error-term $\veps>0$, each player has a pure (subgame-perfect) $\veps$-optimal strategy. Interestingly, a 0-optimal strategy does not always exist. The $\veps$-optimal strategies are robust in the sense that they are $2\veps$-optimal on all finite but sufficiently long horizons, and also $2\veps$-optimal in the discounted version of the game provided that the discount factor is close to 1. We derive results on the analytic and structural properties of the value and the $\veps$-optimal strategies. Moreover, we examine the performance of the finite truncation strategies, which are easy to calculate and to implement. We devote special attention to the important time-homogeneous case, where additional results hold.

cs.GT↗

arXiv2020

Search for a moving target in a competitive environment

We consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.

math.OC↗

arXiv2019

Strong Convergence of Forward-Backward-Forward Methods for Pseudo-monotone Variational Inequalities with Applications to Dynamic User Equilibrium in Traffic Networks

In infinite-dimensional Hilbert spaces we device a class of strongly convergent primal-dual schemes for solving variational inequalities defined by a Lipschitz continuous and pseudomonote map. Our novel numerical scheme is based on Tseng's forward-backward-forward scheme, which is known to display weak convergence, unless very strong global monotonicity assumptions are made on the involved operators. We provide a simple augmentation of this algorithm which is computationally cheap and still guarantees strong convergence to a minimal norm solution of the underlying problem. We provide an adaptive extension of the algorithm, freeing us from requiring knowledge of the global Lipschitz constant. We test the performance of the algorithm in the computationally challenging task to find dynamic user equilibria in traffic networks and verify that our scheme is at least competitive to state-of-the-art solvers, and in some case even improve upon them.

math.OC↗

arXiv2018

Multi-agent online learning in time-varying games

We examine the long-run behavior of multi-agent online learning in games that evolve over time. Specifically, we focus on a wide class of policies based on mirror descent, and we show that the induced sequence of play (a) converges to Nash equilibrium in time-varying games that stabilize in the long run to a strictly monotone limit; and (b) it stays asymptotically close to the evolving equilibrium of the sequence of stage games (assuming they are strongly monotone). Our results apply to both gradient-based and payoff-based feedback - i.e., the "bandit feedback" case where players only get to observe the payoffs of their chosen actions.

cs.GT↗