Research Projects

Online convex optimization (OCO) is a framework that has gained significant attention in the past decade, used to model problems in domains such as portfolio selection, demand response in power systems, and spam filtering. OCO consists of T number of game iterations where an online player selects an action from a convex subset of R^n, K, at each iteration t. The online player learns the convex cost/loss function f_t after the selection, using existing algorithms like gradient descent and mirrored descent. The most general setting in OCO is when the online player only has information about the cost functions in previous iterations. However, the environment around us indicates that cost functions may have some pattern, providing estimates about future iterations. Lesage-Landry et al. have elaborated on the example of demand response (DR) in power systems, where instructions sent by DR aggregators are decided upon based on past observations, weather forecasts, or load patterns. They have presented a predictive online convex optimization (POCO) framework, which applies a predictive step based on the estimated gradient of the next iteration's cost function, leading to strict improvement over the OCO update. Valls et al. studied online convex optimization problems with online constraints and additive perturbations, revealing the cost function f_t and the associated perturbation b_t^j when the online player chooses an action from K. They introduced an algorithm based on regularized primal-dual proximal gradient method, obtaining optimal rates and better bounds for regret and constraint violation.

0