arXiv subjects

Hsu Kao

Publications and source records attributed to Hsu Kao.

4 recordsLinked to original sources

arXiv2023

Nonlinear Consensus for Distributed Optimization

Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider nonlinear consensus schemes with a set of time-varying and agent-dependent monotonic Lipschitz nonlinear transformations, where we note the operation is a subprojection onto the consensus plane, which has been identified via stochastic approximation theory. For the proposed nonlinear consensus schemes, we establish convergence when combined with the NEXT algorithm [Lorenzo and Scutari, 2016], and analyze the convergence rate when combined with the DGD algorithm [Nedić and Ozdaglar, 2009]. In addition, we show that convergence can still be guaranteed even though column stochasticity is relaxed for the gossip of the primal variable, and then couple this with nonlinear transformations to show that as a result one can choose any point within the "shrunk cube hull" spanned from neighbors' variables during the consensus step. We perform numerical simulations to demonstrate the different consensus schemes proposed in the paper can outperform the traditional linear scheme.

math.OC↗

arXiv2021

Decentralized Cooperative Reinforcement Learning with Hierarchical Information Structure

Multi-agent reinforcement learning (MARL) problems are challenging due to information asymmetry. To overcome this challenge, existing methods often require high level of coordination or communication between the agents. We consider two-agent multi-armed bandits (MABs) and Markov decision processes (MDPs) with a hierarchical information structure arising in applications, which we exploit to propose simpler and more efficient algorithms that require no coordination or communication. In the structure, in each step the ``leader" chooses her action first, and then the ``follower" decides his action after observing the leader's action. The two agents observe the same reward (and the same state transition in the MDP setting) that depends on their joint action. For the bandit setting, we propose a hierarchical bandit algorithm that achieves a near-optimal gap-independent regret of $\widetilde{\mathcal{O}}(\sqrt{ABT})$ and a near-optimal gap-dependent regret of $\mathcal{O}(\log(T))$, where $A$ and $B$ are the numbers of actions of the leader and the follower, respectively, and $T$ is the number of steps. We further extend to the case of multiple followers and the case with a deep hierarchy, where we both obtain near-optimal regret bounds. For the MDP setting, we obtain $\widetilde{\mathcal{O}}(\sqrt{H^7S^2ABT})$ regret, where $H$ is the number of steps per episode, $S$ is the number of states, $T$ is the number of episodes. This matches the existing lower bound in terms of $A, B$, and $T$.

cs.LG↗

arXiv2021

Common Information based Approximate State Representations in Multi-Agent Reinforcement Learning

Due to information asymmetry, finding optimal policies for Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) is hard with the complexity growing doubly exponentially in the horizon length. The challenge increases greatly in the multi-agent reinforcement learning (MARL) setting where the transition probabilities, observation kernel, and reward function are unknown. Here, we develop a general compression framework with approximate common and private state representations, based on which decentralized policies can be constructed. We derive the optimality gap of executing dynamic programming (DP) with the approximate states in terms of the approximation error parameters and the remaining time steps. When the compression is exact (no error), the resulting DP is equivalent to the one in existing work. Our general framework generalizes a number of methods proposed in the literature. The results shed light on designing practically useful deep-MARL network structures under the "centralized learning distributed execution" scheme.

cs.LG↗

arXiv2021

Localization and Approximations for Distributed Non-convex Optimization

Distributed optimization has many applications, in communication networks, sensor networks, signal processing, machine learning, and artificial intelligence. Methods for distributed convex optimization are widely investigated, while those for non-convex objectives are not well understood. One of the first non-convex distributed optimization frameworks over an arbitrary interaction graph was proposed by Di Lorenzo and Scutari [IEEE Trans. on Signal and Information Processing over Network, 2 (2016), pp. 120-136], which iteratively applies a combination of local optimization with convex approximations and local averaging. We generalize the existing results in two ways. In the case when the decision variables are separable such that there is partial dependency in the objectives, we reduce the communication complexity of the algorithm so that nodes only keep and communicate local variables instead of the whole vector of variables. In addition, we relax the assumption that the objectives' gradients are bounded and Lipschitz by means of successive proximal approximations. Having developed the methodology, we then discuss many ways to apply our algorithmic framework to resource allocation problems in multi-cellular networks, where the two generalizations are found useful and practical. Simulation results show the superiority of our resource allocation algorithms over naive single cell methods, and furthermore, our approximation framework lead to algorithms that are numerically more stable.

math.OC↗