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 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.

We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $\Omega(\sqrt{T})$ for any strategy, we conclude that DPDS is order optimal up to a $\sqrt{\log{T}}$ term. We evaluate the performance of DPDS empirically in the context of virtual trading in wholesale electricity markets by using historical data from the New York market. Empirical results show that DPDS consistently outperforms benchmark heuristic methods that are derived from machine learning and online learning approaches.

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.

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled replacement. In contrast, sampling replacement is far less understood, yet in practice it is very common, often easier to implement, and usually performs better. In this paper, we provide competitive convergence guarantees for without-replacement sampling under several scenarios, focusing on the natural regime of few passes over the data. Moreover, we describe a useful application of these results in the context of distributed optimization with randomly-partitioned data, yielding a nearly-optimal algorithm for regularized least squares (in terms of both communication complexity and runtime complexity) under broad parameter regimes. Our proof techniques combine ideas from stochastic optimization, adversarial online learning and transductive learning theory, and can potentially be applied to other stochastic optimization and learning problems.

Towards learning programs from data, we introduce the problem of sampling programs from posterior distributions conditioned on that data. Within this setting, we propose an algorithm that uses a symbolic solver to efficiently sample programs. The proposal combines constraint-based program synthesis with sampling via random parity constraints. We give theoretical guarantees on how well the samples approximate the true posterior, and have empirical results showing the algorithm is efficient in practice, evaluating our approach on 22 program learning problems in the domains of text editing and computer-aided programming.

We introduce the Adaptive Skills, Adaptive Partitions (ASAP) framework that (1) learns skills (i.e., temporally extended actions or options) as well as (2) where to apply them. We believe that both (1) and (2) are necessary for a truly general skill learning framework, which is a key building block needed to scale up to lifelong learning agents. The ASAP framework is also able to solve related new tasks simply by adapting where it applies its existing learned skills. We prove that ASAP converges to a local optimum under natural conditions. Finally, our experimental results, which include a RoboCup domain, demonstrate the ability of ASAP to learn where to reuse skills as well as solve multiple tasks with considerably less experience than solving each task from scratch.

Decision making under uncertainty is commonly modelled as a process of competitive stochastic evidence accumulation to threshold (the drift-diffusion model). However, it is unknown how animals learn these decision thresholds. We examine threshold learning by constructing a reward function that averages over many trials to Wald's cost function that defines decision optimality. These rewards are highly stochastic and hence challenging to optimize, which we address in two ways: first, a simple two-factor reward-modulated learning rule derived from Williams' REINFORCE method for neural networks; and second, Bayesian optimization of the reward function with a Gaussian process. Bayesian optimization converges in fewer trials than REINFORCE but is slower computationally with greater variance. The REINFORCE method is also a better model of acquisition behaviour in animals and a similar learning rule has been proposed for modelling basal ganglia function.

We study a general adversarial online learning problem, in which we are given a decision set X' in a reflexive Banach space X and a sequence of reward vectors in the dual space of X. At each iteration, we choose an action from X', based on the observed sequence of previous rewards. Our goal is to minimize regret, defined as the gap between the realized reward and the reward of the best fixed action in hindsight. Using results from infinite dimensional convex analysis, we generalize the method of Dual Averaging (or Follow the Regularized Leader) to our setting and obtain upper bounds on the worst-case regret that generalize many previous results. Under the assumption of uniformly continuous rewards, we obtain explicit regret bounds in a setting where the decision set is the set of probability distributions on a compact metric space S. Importantly, we make no convexity assumptions on either the set S or the reward functions. We also prove a general lower bound on the worst-case regret for any online algorithm. We then apply these results to the problem of learning in repeated two-player zero-sum games on compact metric spaces. In doing so, we first prove that if both players play a Hannan-consistent strategy, then with probability 1 the empirical distributions of play weakly converge to the set of Nash equilibria of the game. We then show that, under mild assumptions, Dual Averaging on the (infinite-dimensional) space of probability distributions indeed achieves Hannan-consistency.

Many practical perception systems exist within larger processes which often include interactions with users or additional components that are capable of evaluating the quality of predicted solutions. In these contexts, it is beneficial to provide these oracle mechanisms with multiple highly likely hypotheses rather than a single prediction. In this work, we pose the task of producing multiple outputs as a learning problem over an ensemble of deep networks -- introducing a novel stochastic gradient descent based approach to minimize the loss with respect to an oracle. Our method is simple to implement, agnostic to both architecture and loss function, and parameter-free. Our approach achieves lower oracle error compared to existing methods on a wide range of tasks and deep architectures. We also show qualitatively that solutions produced from our approach often provide interpretable representations of task ambiguity.