Online Learning for Changing Environments using Coin Betting

A key challenge in online learning is that classical algorithms can be slow to adapt to changing environments. Recent studies have proposed "meta" algorithms that convert any online learning algorithm to one that is adaptive to changing environments, where the adaptivity is analyzed in a quantity called the strongly-adaptive regret. This paper describes a new meta algorithm that has a strongly-adaptive regret bound that is a factor of $\sqrt{\log(T)}$ better than other algorithms with the same time complexity, where $T$ is the time horizon. We also extend our algorithm to achieve a first-order (i.e., dependent on the observed losses) strongly-adaptive regret bound for the first time, to our knowledge. At its heart is a new parameter-free algorithm for the learning with expert advice (LEA) problem in which experts sometimes do not output advice for consecutive time steps (i.e., \emph{sleeping} experts). This algorithm is derived by a reduction from optimal algorithms for the so-called coin betting problem. Empirical results show that our algorithm outperforms state-of-the-art methods in both learning with expert advice and metric learning scenarios.Comment: submitted to a journal. arXiv admin note: substantial text overlap with arXiv:1610.0457

A Modern Introduction to Online Learning

In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.Comment: Fixed more typos, added more history bits, added local norms bounds for OMD and FTR

Scoring dynamics across professional team sports: tempo, balance and predictability

Despite growing interest in quantifying and modeling the scoring dynamics within professional sports games, relative little is known about what patterns or principles, if any, cut across different sports. Using a comprehensive data set of scoring events in nearly a dozen consecutive seasons of college and professional (American) football, professional hockey, and professional basketball, we identify several common patterns in scoring dynamics. Across these sports, scoring tempo---when scoring events occur---closely follows a common Poisson process, with a sport-specific rate. Similarly, scoring balance---how often a team wins an event---follows a common Bernoulli process, with a parameter that effectively varies with the size of the lead. Combining these processes within a generative model of gameplay, we find they both reproduce the observed dynamics in all four sports and accurately predict game outcomes. These results demonstrate common dynamical patterns underlying within-game scoring dynamics across professional team sports, and suggest specific mechanisms for driving them. We close with a brief discussion of the implications of our results for several popular hypotheses about sports dynamics.Comment: 18 pages, 8 figures, 4 tables, 2 appendice

Towards Fair Disentangled Online Learning for Changing Environments

In the problem of online learning for changing environments, data are sequentially received one after another over time, and their distribution assumptions may vary frequently. Although existing methods demonstrate the effectiveness of their learning algorithms by providing a tight bound on either dynamic regret or adaptive regret, most of them completely ignore learning with model fairness, defined as the statistical parity across different sub-population (e.g., race and gender). Another drawback is that when adapting to a new environment, an online learner needs to update model parameters with a global change, which is costly and inefficient. Inspired by the sparse mechanism shift hypothesis, we claim that changing environments in online learning can be attributed to partial changes in learned parameters that are specific to environments and the rest remain invariant to changing environments. To this end, in this paper, we propose a novel algorithm under the assumption that data collected at each time can be disentangled with two representations, an environment-invariant semantic factor and an environment-specific variation factor. The semantic factor is further used for fair prediction under a group fairness constraint. To evaluate the sequence of model parameters generated by the learner, a novel regret is proposed in which it takes a mixed form of dynamic and static regret metrics followed by a fairness-aware long-term constraint. The detailed analysis provides theoretical guarantees for loss regret and violation of cumulative fairness constraints. Empirical evaluations on real-world datasets demonstrate our proposed method sequentially outperforms baseline methods in model accuracy and fairness.Comment: Accepted by KDD 202