Online Learning Without Prior Information
This work addresses the need for adaptive online learning algorithms without manual tuning, which is incremental as it builds on existing lower bounds and algorithm design.
The paper tackles the problem of online learning algorithms requiring prior data information or manual tuning by establishing new lower bounds on performance and constructing algorithms that match any point on this frontier, achieving optimal tradeoffs without prior information.
The vast majority of optimization and online learning algorithms today require some prior information about the data (often in the form of bounds on gradients or on the optimal parameter value). When this information is not available, these algorithms require laborious manual tuning of various hyperparameters, motivating the search for algorithms that can adapt to the data with no prior information. We describe a frontier of new lower bounds on the performance of such algorithms, reflecting a tradeoff between a term that depends on the optimal parameter value and a term that depends on the gradients' rate of growth. Further, we construct a family of algorithms whose performance matches any desired point on this frontier, which no previous algorithm reaches.