Author

# Lacra Pavel

Bio: Lacra Pavel is an academic researcher from University of Toronto. The author has contributed to research in topics: Nash equilibrium & Game theory. The author has an hindex of 26, co-authored 155 publications receiving 2311 citations.

##### Papers published on a yearly basis

##### Papers

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TL;DR: An asynchronous gossip-based algorithm for finding a Nash equilibrium of a game in a distributed multi-player network designed in such a way that players make decisions based on estimates of the other players' actions obtained from local neighbors is presented.

241 citations

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TL;DR: This paper proposes an augmented gradient-play dynamics with correction, in which players communicate locally only with their neighbors to compute an estimate of the other players’ actions, and exploits incremental passivity properties and shows that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbors.

Abstract: In this paper, we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information on the others’ decisions. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the pseudogradient and assumes perfect information. We consider how to modify it in the case of partial, or networked information between players. We propose an augmented gradient-play dynamics with correction, in which players communicate locally only with their neighbors to compute an estimate of the other players’ actions. We derive the new dynamics based on the reformulation as a multiagent coordination problem over an undirected graph. We exploit incremental passivity properties and show that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbors. Under a strict monotonicity property of the pseudogradient, we show that the augmented gradient-play dynamics converges to consensus on the NE of the game. We further discuss two cases that highlight the tradeoff between properties of the game and the communication graph.

185 citations

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TL;DR: This paper shows that the softmax function is the monotone gradient map of the log-sum-exp function and exploits the inverse temperature parameter to derive the Lipschitz and co-coercivity properties of thesoftmax function.

Abstract: In this paper, we utilize results from convex analysis and monotone operator theory to derive additional properties of the softmax function that have not yet been covered in the existing literature. In particular, we show that the softmax function is the monotone gradient map of the log-sum-exp function. By exploiting this connection, we show that the inverse temperature parameter determines the Lipschitz and co-coercivity properties of the softmax function. We then demonstrate the usefulness of these properties through an application in game-theoretic reinforcement learning.

183 citations

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TL;DR: In this article, a distributed algorithm for computation of a generalized Nash equilibrium (GNE) in non-cooperative games over networks is proposed, where the feasible decision sets of all players are coupled together by a globally shared affine constraint.

178 citations

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TL;DR: In this paper, the authors consider the problem of distributed Nash equilibrium seeking over networks, a setting in which players have limited local information (i.e., instantaneous all-to-all player communication) and consider how to modify this gradient-play dynamics in the case of partial or networked information between players.

Abstract: In this paper we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the pseudo-gradient and assumes perfect information, i.e., instantaneous all-to-all player communication. We consider how to modify this gradient-play dynamics in the case of partial, or networked information between players. We propose an augmented gradient-play dynamics with correction in which players communicate locally only with their neighbours to compute an estimate of the other players' actions. We derive the new dynamics based on the reformulation as a multi-agent coordination problem over an undirected graph. We exploit incremental passivity properties and show that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbours. Under a strict monotonicity property of the pseudo-gradient, we show that the augmented gradient-play dynamics converges to consensus on the NE of the game. We further discuss two cases that highlight the tradeoff between properties of the game and the communication graph.

107 citations

##### Cited by

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01 Jan 2003

2,810 citations

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TL;DR: This paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies which are adaptive, distributed, asynchronous, and verifiably correct.

Abstract: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

2,198 citations

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2,084 citations

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TL;DR: A simply approximate formula for estimating the detailed number of pinning nodes and the magnitude of the coupling strength for a given general complex dynamical network is provided.

541 citations