Session: Splitting methods in multi-agent optimization
Chair: Felipe Atenas
Cluster: Multi-agent Optimization and Games
Talk 1: Decentralized forward-backward splitting methods for composite monotone inclusions
Speaker: David Torregrosa-Belén
Abstract: Splitting algorithms are a class of numerical methods adept at solving the monotone inclusion problem consisting in finding a zero in the sum of a finite number of monotone operators. Until very recently the resolution of problems involving a large number of operators was limited to the use of product space reformulations. In general, these reformulations are not appropriate for distributed implementations, as they usually require the computation of a global sum across all nodes in every iteration. More recently, new splitting schemes suitable for different network topologies have been proposed. In this talk, we will discuss a new family of forward-backward splitting algorithms whose communication pattern is induced by the choice of multiple graphs.
Talk 2: An efficient single loop algorithm for a new class of solvable GNEPs
Speaker: Puya Latafat
Abstract: Despite their extensive use in real-world applications, generalized Nash equilibrium problems (GNEPs) remain challenging to solve. Most existing approaches rely on stringent assumptions or involve double-loop procedures. In this work, we identify a novel structure for the constraint set map that fundamentally differs from Rosen's framework. Additionally, we develop a single-loop algorithm to solve the corresponding GNEP efficiently.
Talk 3: A distributed proximal splitting method with linesearch for locally Lipschitz data
Speaker: Felipe Atenas
Abstract: We consider finitely many agents over a connected network working cooperatively to solve a consensus optimization problem. Each agent owns a private convex cost function with a decomposable structure given by the sum of two terms, one smooth and one nonsmooth. In our decentralized setting, no agent has direct access to the information of the overall network, but instead they can only communicate with their neighbors in the network. We propose a distributed primal-dual splitting method of proximal-gradient type with backtracking linesearch with convergence guarantees to minimizers. Our approach allows gradients to be only locally Lipschitz, relaxing the common assumption of existing methods that require global Lipschitz continuity and predefined stepsizes, making it suitable for problems where global constants are unavailable or difficult to compute.
