Partial monitoring games are repeated games where the learner receives feedback that might be different from adversary's move or even the reward gained by the learner. Recently, a general model of combinatorial partial monitoring (CPM) games was proposed [1], where the learner's action space can be exponentially large and adversary samples its moves from a bounded, continuous space, according to a fixed distribution.

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted parameters, in contrast to the prediction error of the parameters. This loss function was recently introduced [7] and christened Smart Predict-then-Optimize (SPO) loss. Since the SPO loss is nonconvex and noncontinuous, standard results for deriving generalization bounds do not apply. In this work, we provide an assortment of generalization bounds for the SPO loss function. In particular, we derive bounds based on the Natarajan dimension that, in the case of a polyhedral feasible region, scale at most logarithmically in the number of extreme points, but, in the case of a general convex set, have poor dependence on the dimension. By exploiting the structure of the SPO loss function and an additional strong convexity assumption on the feasible region, we can dramatically improve the dependence on the dimension via an analysis and corresponding bounds that are akin to the margin guarantees in classification problems.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Active learning is the task of using labelled data to select additional points to label, with the goal of fitting the most accurate model with a fixed budget of labelled points. In binary classification active learning is known to produce faster rates than passive learning for a broad range of settings. However in regression restrictive structure and tailored methods were previously needed to obtain theoretically superior performance. In this paper we propose an intuitive tree based active learning algorithm for non-parametric regression with provable improvement over random sampling. When implemented with Mondrian Trees our algorithm is tuning parameter free, consistent and minimax optimal for Lipschitz functions.

We prove that, under low noise assumptions, the support vector machine with N m random features (RFSVM) can achieve the learning rate faster than O(1/ m) on a training set with m samples when an optimized feature map is used. Our work extends the previous fast rate analysis of random features method from least square loss to 0-1 loss. We also show that the reweighted feature selection method, which approximates the optimized feature map, helps improve the performance of RFSVM in experiments on a synthetic data set.

Neural Information Processing Systems http://nips.cc/

Active learning is the task of using labelled data to select additional points to label, with the goal of fitting the most accurate model with a fixed budget of labelled points. In binary classification active learning is known to produce faster rates than passive learning for a broad range of settings. However in regression restrictive structure and tailored methods were previously needed to obtain theoretically superior performance. In this paper we propose an intuitive tree based active learning algorithm for non-parametric regression with provable improvement over random sampling. When implemented with Mondrian Trees our algorithm is tuning parameter free, consistent and minimax optimal for Lipschitz functions.

In this paper, we use differential privacy as a lens to examine online learning in both full and partial information settings. The differential privacy framework is, at heart, less about privacy and more about algorithmic stability, and thus has found application in domains well beyond those where information security is central. Here we develop an algorithmic property called one-step differential stability which facilitates a more refined regret analysis for online learning methods. We show that tools from the differential privacy literature can yield regret bounds for many interesting online learning problems including online convex optimization and online linear optimization. Our stability notion is particularly well-suited for deriving first-order regret bounds for follow-the-perturbed-leader algorithms, something that all previous analyses have struggled to achieve. We also generalize the standard max-divergence to obtain a broader class called Tsallis max-divergences. These define stronger notions of stability that are useful in deriving bounds in partial information settings such as multi-armed bandits and bandits with experts.

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted parameters, in contrast to the prediction error of the parameters. This loss function was recently introduced [7] and christened Smart Predict-then-Optimize (SPO) loss. Since the SPO loss is nonconvex and noncontinuous, standard results for deriving generalization bounds do not apply. In this work, we provide an assortment of generalization bounds for the SPO loss function. In particular, we derive bounds based on the Natarajan dimension that, in the case of a polyhedral feasible region, scale at most logarithmically in the number of extreme points, but, in the case of a general convex set, have poor dependence on the dimension. By exploiting the structure of the SPO loss function and an additional strong convexity assumption on the feasible region, we can dramatically improve the dependence on the dimension via an analysis and corresponding bounds that are akin to the margin guarantees in classification problems.