The problem of searching for $L$ anomalous processes among $M$ processes is considered. At each time, the decision maker can observe a subset of $K$ processes (i.e., multiple plays). The measurement drawn when observing a process follows one of two different distributions, depending on whether the process is normal or abnormal. The goal is to design a policy that minimizes the Bayes risk which balances between the sample complexity, detection errors, and the switching cost associated with switching across processes. We develop a policy, dubbed consecutive controlled sensing (CCS), to achieve this goal. On the one hand, by contrast to existing studies on controlled sensing, the CCS policy senses processes consecutively to reduce the switching cost. On the other hand, the policy controls the sensing operation in a closed-loop manner to switch between processes when necessary to guarantee reliable inference. We prove theoretically that CCS is asymptotically optimal in terms of minimizing the Bayes risk as the detection error approaches zero (i.e., the sample complexity increases). Simulation results demonstrate strong performance of CCS in the finite regime as well.
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Machine learning is rapidly becoming a core technology for scientific computing, with numerous opportunities to advance the field of computational fluid dynamics. This paper highlights some of the areas of highest potential impact, including to accelerate direct numerical simulations, to improve turbulence closure modelling, and to develop enhanced reduced-order models. In each of these areas, it is possible to improve machine learning capabilities by incorporating physics into the process, and in turn, to improve the simulation of fluids to uncover new physical understanding. Despite the promise of machine learning described here, we also note that classical methods are often more efficient for many tasks. We also emphasize that in order to harness the full potential of machine learning to improve computational fluid dynamics, it is essential for the community to continue to establish benchmark systems and best practices for open-source software, data sharing, and reproducible research.
Valid online inference is an important problem in contemporary multiple testing research, to which various solutions have been proposed recently. It is well-known that these methods can suffer from a significant loss of power if the null $p$-values are conservative. This occurs frequently, for instance whenever discrete tests are performed. To reduce conservatism, we introduce the method of super-uniformity reward (SURE). This approach works by incorporating information about the individual null cumulative distribution functions (or upper bounds of them), which we assume to be available. Our approach yields several new "rewarded" procedures that theoretically control online error criteria based either on the family-wise error rate (FWER) or the marginal false discovery rate (mFDR). We prove that the rewarded procedures uniformly improve upon the non-rewarded ones, and illustrate their performance for simulated and real data.
This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not known and can only be learned from the training sequences which are available. We further require the probability of the \emph{estimation error} to decay either exponentially or sub-exponentially fast (corresponding respectively to the large and moderate deviations regimes in information theory parlance). Based on the training sequences as well as the test sequence consisting of a single change-point, we design a change-point estimator and further show that this estimator is optimal by establishing matching (strong) converses. This leads to a full characterization of the optimal confidence width (i.e., half the width of the confidence interval within which the true change-point is located at with high probability) as a function of the undetected error, under both the large and moderate deviations regimes.
Computing market equilibria is a problem of both theoretical and applied interest. Much research to date focuses on the case of static Fisher markets with full information on buyers' utility functions and item supplies. Motivated by real-world markets, we consider an online setting: individuals have linear, additive utility functions; items arrive sequentially and must be allocated and priced irrevocably. We define the notion of an online market equilibrium in such a market as time-indexed allocations and prices which guarantee buyer optimality and market clearance in hindsight. We propose a simple, scalable and interpretable allocation and pricing dynamics termed as PACE. When items are drawn i.i.d. from an unknown distribution (with a possibly continuous support), we show that PACE leads to an online market equilibrium asymptotically. In particular, PACE ensures that buyers' time-averaged utilities converge to the equilibrium utilities w.r.t. a static market with item supplies being the unknown distribution and that buyers' time-averaged expenditures converge to their per-period budget. Hence, many desirable properties of market equilibrium-based fair division such as no envy, Pareto optimality, and the proportional-share guarantee are also attained asymptotically in the online setting. Next, we extend the dynamics to handle quasilinear buyer utilities, which gives the first online algorithm for computing first-price pacing equilibria. Finally, numerical experiments on real and synthetic datasets show that the dynamics converges quickly under various metrics.
Evolving diverse sets of high quality solutions has gained increasing interest in the evolutionary computation literature in recent years. With this paper, we contribute to this area of research by examining evolutionary diversity optimisation approaches for the classical Traveling Salesperson Problem (TSP). We study the impact of using different diversity measures for a given set of tours and the ability of evolutionary algorithms to obtain a diverse set of high quality solutions when adopting these measures. Our studies show that a large variety of diverse high quality tours can be achieved by using our approaches. Furthermore, we compare our approaches in terms of theoretical properties and the final set of tours obtained by the evolutionary diversity optimisation algorithm.
In one-class-learning tasks, only the normal case (foreground) can be modeled with data, whereas the variation of all possible anomalies is too erratic to be described by samples. Thus, due to the lack of representative data, the wide-spread discriminative approaches cannot cover such learning tasks, and rather generative models, which attempt to learn the input density of the foreground, are used. However, generative models suffer from a large input dimensionality (as in images) and are typically inefficient learners. We propose to learn the data distribution of the foreground more efficiently with a multi-hypotheses autoencoder. Moreover, the model is criticized by a discriminator, which prevents artificial data modes not supported by data, and enforces diversity across hypotheses. Our multiple-hypothesesbased anomaly detection framework allows the reliable identification of out-of-distribution samples. For anomaly detection on CIFAR-10, it yields up to 3.9% points improvement over previously reported results. On a real anomaly detection task, the approach reduces the error of the baseline models from 6.8% to 1.5%.
There has been a recent explosion in the capabilities of game-playing artificial intelligence. Many classes of tasks, from video games to motor control to board games, are now solvable by fairly generic algorithms, based on deep learning and reinforcement learning, that learn to play from experience with minimal prior knowledge. However, these machines often do not win through intelligence alone -- they possess vastly superior speed and precision, allowing them to act in ways a human never could. To level the playing field, we restrict the machine's reaction time to a human level, and find that standard deep reinforcement learning methods quickly drop in performance. We propose a solution to the action delay problem inspired by human perception -- to endow agents with a neural predictive model of the environment which "undoes" the delay inherent in their environment -- and demonstrate its efficacy against professional players in Super Smash Bros. Melee, a popular console fighting game.
Recent studies have shown the vulnerability of reinforcement learning (RL) models in noisy settings. The sources of noises differ across scenarios. For instance, in practice, the observed reward channel is often subject to noise (e.g., when observed rewards are collected through sensors), and thus observed rewards may not be credible as a result. Also, in applications such as robotics, a deep reinforcement learning (DRL) algorithm can be manipulated to produce arbitrary errors. In this paper, we consider noisy RL problems where observed rewards by RL agents are generated with a reward confusion matrix. We call such observed rewards as perturbed rewards. We develop an unbiased reward estimator aided robust RL framework that enables RL agents to learn in noisy environments while observing only perturbed rewards. Our framework draws upon approaches for supervised learning with noisy data. The core ideas of our solution include estimating a reward confusion matrix and defining a set of unbiased surrogate rewards. We prove the convergence and sample complexity of our approach. Extensive experiments on different DRL platforms show that policies based on our estimated surrogate reward can achieve higher expected rewards, and converge faster than existing baselines. For instance, the state-of-the-art PPO algorithm is able to obtain 67.5% and 46.7% improvements in average on five Atari games, when the error rates are 10% and 30% respectively.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
We propose an Active Learning approach to image segmentation that exploits geometric priors to streamline the annotation process. We demonstrate this for both background-foreground and multi-class segmentation tasks in 2D images and 3D image volumes. Our approach combines geometric smoothness priors in the image space with more traditional uncertainty measures to estimate which pixels or voxels are most in need of annotation. For multi-class settings, we additionally introduce two novel criteria for uncertainty. In the 3D case, we use the resulting uncertainty measure to show the annotator voxels lying on the same planar patch, which makes batch annotation much easier than if they were randomly distributed in the volume. The planar patch is found using a branch-and-bound algorithm that finds a patch with the most informative instances. We evaluate our approach on Electron Microscopy and Magnetic Resonance image volumes, as well as on regular images of horses and faces. We demonstrate a substantial performance increase over state-of-the-art approaches.
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