We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily a cumulative loss. This framework allows us to study a very general class of problems, with applications in statistics, machine learning, and other fields. To solve this problem, we analyze the Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and convex optimization. We give theoretical guarantees for the performance of this algorithm over various classes of functions, and discuss the optimality of these results.

Imitation learning has been commonly applied to solve different tasks in isolation.

Machine learning can impact people with legal or ethical consequences when it is used to automate decisions in areas such as insurance, lending, hiring, and predictive policing. In many of these scenarios, previous decisions have been made that are unfairly biased against certain subpopulations, for example those of a particular race, gender, or sexual orientation. Since this past data may be biased, machine learning predictors must account for this to avoid perpetuating or creating discriminatory practices. In this paper, we develop a framework for modeling fairness using tools from causal inference. Our definition of counterfactual fairness captures the intuition that a decision is fair towards an individual if it the same in (a) the actual world and (b) a counterfactual world where the individual belonged to a different demographic group. We demonstrate our framework on a real-world problem of fair prediction of success in law school.

We introduce an efficient algorithmic framework for model selection in online learning, also known as parameter-free online learning. Departing from previous work, which has focused on highly structured function classes such as nested balls in Hilbert space, we propose a generic meta-algorithm framework that achieves online model selection oracle inequalities under minimal structural assumptions. We give the first computationally efficient parameter-free algorithms that work in arbitrary Banach spaces under mild smoothness assumptions; previous results applied only to Hilbert spaces. We further derive new oracle inequalities for matrix classes, non-nested convex sets, and $\mathbb{R}^{d}$ with generic regularizers. Finally, we generalize these results by providing oracle inequalities for arbitrary non-linear classes in the online supervised learning model. These results are all derived through a unified meta-algorithm scheme using a novel multi-scale algorithm for prediction with expert advice based on random playout, which may be of independent interest.

We develop a nonparametric and online learning algorithm that estimates the triggering functions of a multivariate Hawkes process (MHP). The approach we take approximates the triggering function $f_{i,j}(t)$ by functions in a reproducing kernel Hilbert space (RKHS), and maximizes a time-discretized version of the log-likelihood, with Tikhonov regularization. Theoretically, our algorithm achieves an $\calO(\log T)$ regret bound. Numerical results show that our algorithm offers a competing performance to that of the nonparametric batch learning algorithm, with a run time comparable to the parametric online learning algorithm.

We study online learning with the general notion of transductive regret, that is regret with modification rules applying to expert sequences (as opposed to single experts) that are representable by weighted finite-state transducers. We show how transductive regret generalizes existing notions of regret, including: (1) external regret; (2) internal regret; (3) swap regret; and (4) conditional swap regret. We present a general and efficient online learning algorithm for minimizing transductive regret. We further extend that to design efficient algorithms for the time-selection and sleeping expert settings. A by-product of our study is an algorithm for swap regret, which, under mild assumptions, is more efficient than existing ones, and a substantially more efficient algorithm for time selection swap regret.

Better understanding of the potential benefits of information transfer and representation learning is an important step towards the goal of building intelligent systems that are able to persist in the world and learn over time. In this work, we consider a setting where the learner encounters a stream of tasks but is able to retain only limited information from each encountered task, such as a learned predictor. In contrast to most previous works analyzing this scenario, we do not make any distributional assumptions on the task generating process. Instead, we formulate a complexity measure that captures the diversity of the observed tasks. We provide a lifelong learning algorithm with error guarantees for every observed task (rather than on average). We show sample complexity reductions in comparison to solving every task in isolation in terms of our task complexity measure. Further, our algorithmic framework can naturally be viewed as learning a representation from encountered tasks with a neural network.

Most online optimization algorithms focus on one of two things: performing well in adversarial settings by adapting to unknown data parameters (such as Lipschitz constants), typically achieving $O(\sqrt{T})$ regret, or performing well in stochastic settings where they can leverage some structure in the losses (such as strong convexity), typically achieving $O(\log(T))$ regret. Algorithms that focus on the former problem hitherto achieved $O(\sqrt{T})$ in the stochastic setting rather than $O(\log(T))$. Here we introduce an online optimization algorithm that achieves $O(\log^4(T))$ regret in a wide class of stochastic settings while gracefully degrading to the optimal $O(\sqrt{T})$ regret in adversarial settings (up to logarithmic factors). Our algorithm does not require any prior knowledge about the data or tuning of parameters to achieve superior performance.

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

The goal of minimizing misclassification error on a training set is often just one of several real-world goals that might be defined on different datasets. For example, one may require a classifier to also make positive predictions at some specified rate for some subpopulation (fairness), or to achieve a specified empirical recall. Other real-world goals include reducing churn with respect to a previously deployed model, or stabilizing online training. In this paper we propose handling multiple goals on multiple datasets by training with dataset constraints, using the ramp penalty to accurately quantify costs, and present an efficient algorithm to approximately optimize the resulting non-convex constrained optimization problem. Experiments on both benchmark and real-world industry datasets demonstrate the effectiveness of our approach.