• Abstract

In online learning, the data is provided in sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online learning problems: online linear optimization, adversarial bandit, and adversarial linear bandit. For each problem, we extend the discrete-time algorithm to the continuous-time setting and provide a concise proof of the optimal regret bound.

• General Summary

• Abstract

We present the development and analysis of a reinforcement learning algorithm designed to solve continuous-space mean field game (MFG) and mean field control (MFC) problems in a unified manner. The proposed approach pairs the actor-critic (AC) paradigm with a representation of the mean field distribution via a parameterized score function, which can be efficiently updated in an online fashion, and uses Langevin dynamics to obtain samples from the resulting distribution. The AC agent and the score function are updated iteratively to converge, either to the MFG equilibrium or the MFC optimum for a given mean field problem, depending on the choice of learning rates. A straightforward modification of the algorithm allows us to solve mixed mean field control games. The performance of our algorithm is evaluated using linear-quadratic benchmarks in the asymptotic infinite horizon framework.

• General Summary