Bias-Robust Bayesian Optimization via Dueling Bandits

We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueling bandit model. Then we propose a novel approach for dueling bandits based on information-directed sampling (IDS). Thereby, we obtain the first efficient kernelized algorithm for dueling bandits that comes with cumulative regret guarantees. Our analysis further generalizes a previously proposed semi-parametric linear bandit model to non-linear reward functions, and uncovers interesting links to doubly-robust estimation

Information Directed Sampling and Bandits with Heteroscedastic Noise

In the stochastic bandit problem, the goal is to maximize an unknown function via a sequence of noisy evaluations. Typically, the observation noise is assumed to be independent of the evaluation point and to satisfy a tail bound uniformly on the domain; a restrictive assumption for many applications. In this work, we consider bandits with heteroscedastic noise, where we explicitly allow the noise distribution to depend on the evaluation point. We show that this leads to new trade-offs for information and regret, which are not taken into account by existing approaches like upper confidence bound algorithms (UCB) or Thompson Sampling. To address these shortcomings, we introduce a frequentist regret analysis framework, that is similar to the Bayesian framework of Russo and Van Roy (2014), and we prove a new high-probability regret bound for general, possibly randomized policies, which depends on a quantity we refer to as regret-information ratio. From this bound, we define a frequentist version of Information Directed Sampling (IDS) to minimize the regret-information ratio over all possible action sampling distributions. This further relies on concentration inequalities for online least squares regression in separable Hilbert spaces, which we generalize to the case of heteroscedastic noise. We then formulate several variants of IDS for linear and reproducing kernel Hilbert space response functions, yielding novel algorithms for Bayesian optimization. We also prove frequentist regret bounds, which in the homoscedastic case recover known bounds for UCB, but can be much better when the noise is heteroscedastic. Empirically, we demonstrate in a linear setting with heteroscedastic noise, that some of our methods can outperform UCB and Thompson Sampling, while staying competitive when the noise is homoscedastic.Comment: Figure 1a,2a update

Stochastic Bandits with Context Distributions

We introduce a stochastic contextual bandit model where at each time step the environment chooses a distribution over a context set and samples the context from this distribution. The learner observes only the context distribution while the exact context realization remains hidden. This allows for a broad range of applications where the context is stochastic or when the learner needs to predict the context. We leverage the UCB algorithm to this setting and show that it achieves an order-optimal high-probability bound on the cumulative regret for linear and kernelized reward functions. Our results strictly generalize previous work in the sense that both our model and the algorithm reduce to the standard setting when the environment chooses only Dirac delta distributions and therefore provides the exact context to the learner. We further analyze a variant where the learner observes the realized context after choosing the action. Finally, we demonstrate the proposed method on synthetic and real-world datasets.Comment: Accepted at NeurIPS 201

Poster: Debugging Inputs

Program failures are often caused by invalid inputs, for instance due to input corruption. To obtain the passing input, one needs to debug the data. In this paper we present a generic technique called ddmax that (1) identifies which parts of the input data prevent processing, and (2) recovers as much of the (valuable) input data as possible. To the best of our knowledge, ddmax is the first approach that fixes faults in the input data without requiring program analysis. In our evaluation, ddmax repaired about 69% of input files and recovered about 78% of data within one minute per input

Linear Partial Monitoring for Sequential Decision-Making: Algorithms, Regret Bounds and Applications

Partial monitoring is an expressive framework for sequential decision-making with an abundance of applications, including graph-structured and dueling bandits, dynamic pricing and transductive feedback models. We survey and extend recent results on the linear formulation of partial monitoring that naturally generalizes the standard linear bandit setting. The main result is that a single algorithm, information-directed sampling (IDS), is (nearly) worst-case rate optimal in all finite-action games. We present a simple and unified analysis of stochastic partial monitoring, and further extend the model to the contextual and kernelized setting

Information Directed Sampling for Linear Partial Monitoring

Partial monitoring is a rich framework for sequential decision making under uncertainty that generalizes many well known bandit models, including linear, combinatorial and dueling bandits. We introduce information directed sampling (IDS) for stochastic partial monitoring with a linear reward and observation structure. IDS achieves adaptive worst-case regret rates that depend on precise observability conditions of the game. Moreover, we prove lower bounds that classify the minimax regret of all finite games into four possible regimes. IDS achieves the optimal rate in all cases up to logarithmic factors, without tuning any hyper-parameters. We further extend our results to the contextual and the kernelized setting, which significantly increases the range of possible applications

Locating Faults with Program Slicing: An Empirical Analysis

Statistical fault localization is an easily deployed technique for quickly determining candidates for faulty code locations. If a human programmer has to search the fault beyond the top candidate locations, though, more traditional techniques of following dependencies along dynamic slices may be better suited. In a large study of 457 bugs (369 single faults and 88 multiple faults) in 46 open source C programs, we compare the effectiveness of statistical fault localization against dynamic slicing. For single faults, we find that dynamic slicing was eight percentage points more effective than the best performing statistical debugging formula; for 66% of the bugs, dynamic slicing finds the fault earlier than the best performing statistical debugging formula. In our evaluation, dynamic slicing is more effective for programs with single fault, but statistical debugging performs better on multiple faults. Best results, however, are obtained by a hybrid approach: If programmers first examine at most the top five most suspicious locations from statistical debugging, and then switch to dynamic slices, on average, they will need to examine 15% (30 lines) of the code. These findings hold for 18 most effective statistical debugging formulas and our results are independent of the number of faults (i.e. single or multiple faults) and error type (i.e. artificial or real errors)

Distributionally Robust Bayesian Optimization

Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is worst-case robust under a specified distributional shift of an uncontrolled covariate. In this paper, we study such a problem when the distributional shift is measured via the maximum mean discrepancy (MMD). For the setting of zeroth-order, noisy optimization, we present a novel distributionally robust Bayesian optimization algorithm (DRBO). Our algorithm provably obtains sub-linear robust regret in various settings that differ in how the uncertain covariate is observed. We demonstrate the robust performance of our method on both synthetic and real-world benchmarks.Comment: Accepted at AISTATS 202

コクサイ レンケイ ニヨル カクユウゴウロ ジツゲン オ メザシタ プラズマ タイコウロ ザイリョウ ジュミョウ ヒョウカ コード ノ カイハツ

A 13CH4 injection experiment with a test limiter in TEXTOR is modeled by EDDY and ERO for the purpose of code-code benchmarking. The 2D patterns of CH emission of both codes agree with the experiment. The 13C deposition patterns on the limiter surface are reproduced assuming negligible effective sticking (S=0) for returning hydrocarbons. The 13C deposition efficiency decreases with increasing injection time, and it reaches a steady state value accompanied by a depth profile of 13C. The measured 13C deposition efficiency (~0.1%) is reproduced, assuming negligible sticking of returning hydrocarbons and high re-erosion yield of redeposited carbons (of the order of 10 times larger than graphite). The sticking probability and re-erosion yield are still unknown parameters, which determine erosion and deposition of plasma facing materials

Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces

Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we propose an algorithm (LineBO) that restricts the problem to a sequence of iteratively chosen one-dimensional sub-problems that can be solved efficiently. We show that our algorithm converges globally and obtains a fast local rate when the function is strongly convex. Further, if the objective has an invariant subspace, our method automatically adapts to the effective dimension without changing the algorithm. When combined with the SafeOpt algorithm to solve the sub-problems, we obtain the first safe Bayesian optimization algorithm with theoretical guarantees applicable in high-dimensional settings. We evaluate our method on multiple synthetic benchmarks, where we obtain competitive performance. Further, we deploy our algorithm to optimize the beam intensity of the Swiss Free Electron Laser with up to 40 parameters while satisfying safe operation constraints