Online Convex Optimization with Switching Costs: Algorithms and Performance

Abstract

In this paper, we study the problem of online convex optimization with switching costs (SOCO) that appears in diverse scenarios including power management, video streaming, resource allocation, etc. SOCO refers to online decision problems when the agent incurs both hitting cost and an additional switching cost of changing decisions. We adopt the universal dynamic regret as the performance metric, and consider the case when loss functions are unknown when making decisions. Previous results rely on the assumptions on loss function, e.g., linearity and smoothness, or prior knowledge of regularity measures, e.g., path length of the comparator sequence. In this paper, we propose an algorithm IOMD-SOCO that applies to general convex loss function, and show that the algorithm achieves an order-optimal universal dynamic regret bound. We also propose its parameter-free versions, i.e., without requiring the prior knowledge of path length of the comparator sequence, and achieve the same-order regret bound. We are the first to provide dynamic regret bounds for SOCO with general convex loss functions via parameter-free algorithm. Our numerical experiments show that IOMD-SOCO indeed achieves a substantial performance improvement.