2 research outputs found
Multi-agent constrained optimization of a strongly convex function over time-varying directed networks
We consider cooperative multi-agent consensus optimization problems over both
static and time-varying communication networks, where only local communications
are allowed. The objective is to minimize the sum of agent-specific possibly
non-smooth composite convex functions over agent-specific private conic
constraint sets; hence, the optimal consensus decision should lie in the
intersection of these private sets. Assuming the sum function is strongly
convex, we provide convergence rates in suboptimality, infeasibility and
consensus violation; examine the effect of underlying network topology on the
convergence rates of the proposed decentralized algorithms
Distributed Variable Sample-Size Gradient-response and Best-response Schemes for Stochastic Nash Equilibrium Problems over Graphs
This paper considers a stochastic Nash game in which each player minimizes an
expectation valued composite objective. We make the following contributions.
(I) Under suitable monotonicity assumptions on the concatenated gradient map,
we derive optimal rate statements and oracle complexity bounds for the proposed
variable sample-size proximal stochastic gradient-response (VS-PGR) scheme when
the sample-size increases at a geometric rate. If the sample-size increases at
a polynomial rate of degree , the mean-squared errordecays at a
corresponding polynomial rate while the iteration and oracle complexities to
obtain an -NE are and
, respectively. (II) We then overlay (VS-PGR)
with a consensus phase with a view towards developing distributed protocols for
aggregative stochastic Nash games. In the resulting scheme, when the
sample-size and the consensus steps grow at a geometric and linear rate,
computing an -NE requires similar iteration and oracle complexities
to (VS-PGR) with a communication complexity of
; (III) Under a suitable contractive property
associated with the proximal best-response (BR) map, we design a variable
sample-size proximal BR (VS-PBR) scheme, where each player solves a
sample-average BR problem. Akin to (I), we also give the rate statements,
oracle and iteration complexity bounds. (IV) Akin to (II), the distributed
variant achieves similar iteration and oracle complexities to the centralized
(VS-PBR) with a communication complexity of
when the communication rounds per iteration increase at a linear rate. Finally,
we present some preliminary numerics to provide empirical support for the rate
and complexity statements