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

Online Learning with an Almost Perfect Expert

We study the multiclass online learning problem where a forecaster makes a sequence of predictions using the advice of $n$ experts. Our main contribution is to analyze the regime where the best expert makes at most $b$ mistakes and to show that when $b = o(\log_4{n})$, the expected number of mistakes made by the optimal forecaster is at most $\log_4{n} + o(\log_4{n})$. We also describe an adversary strategy showing that this bound is tight and that the worst case is attained for binary prediction

Tight Lower Bounds for Multiplicative Weights Algorithmic Families

We study the fundamental problem of prediction with expert advice and develop regret lower bounds for a large family of algorithms for this problem. We develop simple adversarial primitives, that lend themselves to various combinations leading to sharp lower bounds for many algorithmic families. We use these primitives to show that the classic Multiplicative Weights Algorithm (MWA) has a regret of $\sqrt{\frac{T \ln k}{2}}$, there by completely closing the gap between upper and lower bounds. We further show a regret lower bound of $\frac{2}{3}\sqrt{\frac{T\ln k}{2}}$ for a much more general family of algorithms than MWA, where the learning rate can be arbitrarily varied over time, or even picked from arbitrary distributions over time. We also use our primitives to construct adversaries in the geometric horizon setting for MWA to precisely characterize the regret at $\frac{0.391}{\sqrt{\delta}}$ for the case of $2$ experts and a lower bound of $\frac{1}{2}\sqrt{\frac{\ln k}{2\delta}}$ for the case of arbitrary number of experts $k$

Adversarial Calibrated Regression for Online Decision Making

Accurately estimating uncertainty is an essential component of decision-making and forecasting in machine learning. However, existing uncertainty estimation methods may fail when data no longer follows the distribution seen during training. Here, we introduce online uncertainty estimation algorithms that are guaranteed to be reliable on arbitrary streams of data points, including data chosen by an adversary. Specifically, our algorithms perform post-hoc recalibration of a black-box regression model and produce outputs that are provably calibrated -- i.e., an 80% confidence interval will contain the true outcome 80% of the time -- and that have low regret relative to the learning objective of the base model. We apply our algorithms in the context of Bayesian optimization, an online model-based decision-making task in which the data distribution shifts over time, and observe accelerated convergence to improved optima. Our results suggest that robust uncertainty quantification has the potential to improve online decision-making.Comment: arXiv admin note: text overlap with arXiv:1607.0359

Pruning neural networks using multi-armed bandits

The successful application of deep learning has led to increasing expectations of their use in embedded systems. This in turn, has created the need to find ways of reducing the size of neural networks. Decreasing the size of a neural network requires deciding which weights should be removed without compromising accuracy, which is analogous to the kind of problems addressed by multi-arm bandits. Hence, this paper explores the use of multi-armed bandits for reducing the number of parameters of a neural network. Different multi-armed bandit algorithms, namely e-greedy, win-stay, lose-shift, UCB1, KL-UCB, BayesUCB, UGapEb, Successive Rejects and Thompson sampling are evaluated and their performance compared to existing approaches. The results show that multi- armed bandit pruning methods, especially those based on UCB, outperform other pruning methods