TY - GEN
T1 - A distributed adaptive steplength stochastic approximation method for monotone stochastic Nash Games
AU - Yousefian, Farzad
AU - Nedic, Angelia
AU - Shanbhag, Uday V.
PY - 2013
Y1 - 2013
N2 - We consider a distributed stochastic approximation (SA) scheme for computing an equilibrium of a stochastic Nash game. Standard SA schemes employ diminishing steplength sequences that are square summable but not summable. Such requirements provide a little or no guidance for how to leverage Lipschitzian and monotonicity properties of the problem and naive choices (such as γk = 1/k) generally do not preform uniformly well on a breadth of problems. While a centralized adaptive stepsize SA scheme is proposed in [1] for the optimization framework, such a scheme provides no freedom for the agents in choosing their own stepsizes. Thus, a direct application of centralized stepsize schemes is impractical in solving Nash games. Furthermore, extensions to game-theoretic regimes where players may independently choose steplength sequences are limited to recent work by Koshal et al. [2]. Motivated by these shortcomings, we present a distributed algorithm in which each player updates his steplength based on the previous steplength and some problem parameters. The steplength rules are derived from minimizing an upper bound of the errors associated with players' decisions. It is shown that these rules generate sequences that converge almost surely to an equilibrium of the stochastic Nash game. Importantly, variants of this rule are suggested where players independently select steplength sequences while abiding by an overall coordination requirement. Preliminary numerical results are seen to be promising.
AB - We consider a distributed stochastic approximation (SA) scheme for computing an equilibrium of a stochastic Nash game. Standard SA schemes employ diminishing steplength sequences that are square summable but not summable. Such requirements provide a little or no guidance for how to leverage Lipschitzian and monotonicity properties of the problem and naive choices (such as γk = 1/k) generally do not preform uniformly well on a breadth of problems. While a centralized adaptive stepsize SA scheme is proposed in [1] for the optimization framework, such a scheme provides no freedom for the agents in choosing their own stepsizes. Thus, a direct application of centralized stepsize schemes is impractical in solving Nash games. Furthermore, extensions to game-theoretic regimes where players may independently choose steplength sequences are limited to recent work by Koshal et al. [2]. Motivated by these shortcomings, we present a distributed algorithm in which each player updates his steplength based on the previous steplength and some problem parameters. The steplength rules are derived from minimizing an upper bound of the errors associated with players' decisions. It is shown that these rules generate sequences that converge almost surely to an equilibrium of the stochastic Nash game. Importantly, variants of this rule are suggested where players independently select steplength sequences while abiding by an overall coordination requirement. Preliminary numerical results are seen to be promising.
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U2 - 10.1109/acc.2013.6580575
DO - 10.1109/acc.2013.6580575
M3 - Conference contribution
AN - SCOPUS:84883524862
SN - 9781479901777
T3 - Proceedings of the American Control Conference
SP - 4765
EP - 4770
BT - 2013 American Control Conference, ACC 2013
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2013 1st American Control Conference, ACC 2013
Y2 - 17 June 2013 through 19 June 2013
ER -