Online Convex Optimization
In recent years, convex optimization and the notion of regret minimization in games, have been combined and applied to machine learning in a general framework called online convex optimization. For more information see graduate text book on online convex optimization in machine learning, or survey on the convex optimization approach to regret minimization. Our research spans efficient online algorithms as well as matrix prediction algorithms, and decision making under uncertainty and continuous multi-armed bandits.
Optimization for Machine Learning
Machine learning moves us from the custom-designed algorithm to generic models, such as neural networks, that are trained by optimization algorithms. Some of the most useful and efficient methods for training convex as well as non-convex methods that we have worked on include:
- The AdaGrad algorithm, and the technique of adaptive preconditioning.
- Sublinear optimization algorithms for linear classification, training support vector machines, semidefinite optimization and to other problems.
- Projection-free algorithms for online learning in the context of recommender systems, and the first linearly convergent projection-free algorithm.
Control and Reinforcement Learning
Bringing tools from online learning and improper convex relaxations, our group has been working on new algorithms for control and prediction in time series that include:
- The Spectral Filtering, technique, and its application to assymetric linear dynamical systems.
- Learnning auto-regressive moving-average time series with adversarial nosie.
- Maximum-entropy exploration in partially observed and/or approximated Markov Decision Processes.