Parameter-free Online Linear Optimization with Side Information via Universal Coin Betting
This work addresses the challenge of optimizing without prior parameter tuning in online settings with side information, offering incremental improvements for machine learning and information theory applications.
The authors tackled the problem of parameter-free online linear optimization with side information by proposing algorithms that adapt to adversarial sequences using coin betting and universal compression techniques, achieving computationally efficient performance over all adaptive algorithms with tree-structured side information up to a given maximum order.
A class of parameter-free online linear optimization algorithms is proposed that harnesses the structure of an adversarial sequence by adapting to some side information. These algorithms combine the reduction technique of Orabona and P{á}l (2016) for adapting coin betting algorithms for online linear optimization with universal compression techniques in information theory for incorporating sequential side information to coin betting. Concrete examples are studied in which the side information has a tree structure and consists of quantized values of the previous symbols of the adversarial sequence, including fixed-order and variable-order Markov cases. By modifying the context-tree weighting technique of Willems, Shtarkov, and Tjalkens (1995), the proposed algorithm is further refined to achieve the best performance over all adaptive algorithms with tree-structured side information of a given maximum order in a computationally efficient manner.