Estimating Uncertainty Online Against an Adversary

Assessing uncertainty is an important step towards ensuring the safety and reliability of machine learning systems. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e.g. when the data distribution differs from the one seen at training time. Here, we propose techniques that assess a classification algorithm's uncertainty via calibrated probabilities (i.e. probabilities that match empirical outcome frequencies in the long run) and which are guaranteed to be reliable (i.e. accurate and calibrated) on out-of-distribution input, including input generated by an adversary. This represents an extension of classical online learning that handles uncertainty in addition to guaranteeing accuracy under adversarial assumptions. We establish formal guarantees for our methods, and we validate them on two real-world problems: question answering and medical diagnosis from genomic data

Learning from Data with Heterogeneous Noise using SGD

We consider learning from data of variable quality that may be obtained from different heterogeneous sources. Addressing learning from heterogeneous data in its full generality is a challenging problem. In this paper, we adopt instead a model in which data is observed through heterogeneous noise, where the noise level reflects the quality of the data source. We study how to use stochastic gradient algorithms to learn in this model. Our study is motivated by two concrete examples where this problem arises naturally: learning with local differential privacy based on data from multiple sources with different privacy requirements, and learning from data with labels of variable quality. The main contribution of this paper is to identify how heterogeneous noise impacts performance. We show that given two datasets with heterogeneous noise, the order in which to use them in standard SGD depends on the learning rate. We propose a method for changing the learning rate as a function of the heterogeneity, and prove new regret bounds for our method in two cases of interest. Experiments on real data show that our method performs better than using a single learning rate and using only the less noisy of the two datasets when the noise level is low to moderate

Bandit Models of Human Behavior: Reward Processing in Mental Disorders

Drawing an inspiration from behavioral studies of human decision making, we propose here a general parametric framework for multi-armed bandit problem, which extends the standard Thompson Sampling approach to incorporate reward processing biases associated with several neurological and psychiatric conditions, including Parkinson's and Alzheimer's diseases, attention-deficit/hyperactivity disorder (ADHD), addiction, and chronic pain. We demonstrate empirically that the proposed parametric approach can often outperform the baseline Thompson Sampling on a variety of datasets. Moreover, from the behavioral modeling perspective, our parametric framework can be viewed as a first step towards a unifying computational model capturing reward processing abnormalities across multiple mental conditions.Comment: Conference on Artificial General Intelligence, AGI-1

On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine learning tasks. However, it has not been analyzed for non-convex minimization and there still remains a gap between the theory and the practice. In this paper, we analyze gradient descent and stochastic gradient descent with extrapolation for finding an approximate first-order stationary point in smooth non-convex optimization problems. Our convergence upper bounds show that the algorithms with extrapolation can be accelerated than without extrapolation

The Limitations of Optimization from Samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature

Context Attentive Bandits: Contextual Bandit with Restricted Context

We consider a novel formulation of the multi-armed bandit model, which we call the contextual bandit with restricted context, where only a limited number of features can be accessed by the learner at every iteration. This novel formulation is motivated by different online problems arising in clinical trials, recommender systems and attention modeling. Herein, we adapt the standard multi-armed bandit algorithm known as Thompson Sampling to take advantage of our restricted context setting, and propose two novel algorithms, called the Thompson Sampling with Restricted Context(TSRC) and the Windows Thompson Sampling with Restricted Context(WTSRC), for handling stationary and nonstationary environments, respectively. Our empirical results demonstrate advantages of the proposed approaches on several real-life datasetsComment: IJCAI 201