Improved Space Bounds for Learning with Experts

Understanding the performance of learning algorithms under information constraints is a fundamental research direction in machine learning. While performance notions such as regret in online learning have been well explored, a recent line of work explores additional constraints in learning, with a particular emphasis on limited memory [Sha14, WS19, MSSV22] (see also Section 3). In this paper, we focus on the online learning with experts problem, a general framework for sequential decision making, with memory constraints. In the online learning with experts problem, an algorithm must make predictions about the outcome of an event for T consecutive days based on the predictions of n experts. The predictions of the algorithm at a time t T can only depend on the information it has received in the previous days as well as the predictions of the experts for day t. After predictions are made, the true outcome is revealed and the algorithm and all experts receive some loss (likely depending on the accuracy of their predictions). In addition to the fact that the online experts problem has found numerous algorithmic applications [AHK12], studying the problem with memory constraints is especially interesting in light of the fact that existing algorithms explicitly track the cumulative loss of every expert and follow the advice of a leading expert, which requires Ω(n) memory. Motivated by this lack of understanding, the online learning with experts problem with memory constraints was recently introduced in [SWXZ22], which studied the case where the losses of the experts form an i.i.d.