A Contextual Bandit Bake-off

Contextual bandit algorithms are essential for solving many real-world interactive machine learning problems. Despite multiple recent successes on statistically and computationally efficient methods, the practical behavior of these algorithms is still poorly understood. We leverage the availability of large numbers of supervised learning datasets to empirically evaluate contextual bandit algorithms, focusing on practical methods that learn by relying on optimization oracles from supervised learning. We find that a recent method (Foster et al., 2018) using optimism under uncertainty works the best overall. A surprisingly close second is a simple greedy baseline that only explores implicitly through the diversity of contexts, followed by a variant of Online Cover (Agarwal et al., 2014) which tends to be more conservative but robust to problem specification by design. Along the way, we also evaluate various components of contextual bandit algorithm design such as loss estimators. Overall, this is a thorough study and review of contextual bandit methodology

Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

Block coordinate descent (BCD) methods are widely-used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can lead to significantly faster BCD methods. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with a sparse dependency between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization

Adaptive Information Gathering via Imitation Learning

In the adaptive information gathering problem, a policy is required to select an informative sensing location using the history of measurements acquired thus far. While there is an extensive amount of prior work investigating effective practical approximations using variants of Shannon's entropy, the efficacy of such policies heavily depends on the geometric distribution of objects in the world. On the other hand, the principled approach of employing online POMDP solvers is rendered impractical by the need to explicitly sample online from a posterior distribution of world maps. We present a novel data-driven imitation learning framework to efficiently train information gathering policies. The policy imitates a clairvoyant oracle - an oracle that at train time has full knowledge about the world map and can compute maximally informative sensing locations. We analyze the learnt policy by showing that offline imitation of a clairvoyant oracle is implicitly equivalent to online oracle execution in conjunction with posterior sampling. This observation allows us to obtain powerful near-optimality guarantees for information gathering problems possessing an adaptive sub-modularity property. As demonstrated on a spectrum of 2D and 3D exploration problems, the trained policies enjoy the best of both worlds - they adapt to different world map distributions while being computationally inexpensive to evaluate.Comment: Robotics Science and Systems, 201