arXiv subjects

Andreas Krause

Publications and source records attributed to Andreas Krause.

At least 217 records · Page 12Linked to original sources

arXiv2021

Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases

Many applications of machine learning on discrete domains, such as learning preference functions in recommender systems or auctions, can be reduced to estimating a set function that is sparse in the Fourier domain. In this work, we present a new family of algorithms for learning Fourier-sparse set functions. They require at most $nk - k \log_2 k + k$ queries (set function evaluations), under mild conditions on the Fourier coefficients, where $n$ is the size of the ground set and $k$ the number of non-zero Fourier coefficients. In contrast to other work that focused on the orthogonal Walsh-Hadamard transform, our novel algorithms operate with recently introduced non-orthogonal Fourier transforms that offer different notions of Fourier-sparsity. These naturally arise when modeling, e.g., sets of items forming substitutes and complements. We demonstrate effectiveness on several real-world applications.

cs.LG↗

arXiv2021

Combining Pessimism with Optimism for Robust and Efficient Model-Based Deep Reinforcement Learning

In real-world tasks, reinforcement learning (RL) agents frequently encounter situations that are not present during training time. To ensure reliable performance, the RL agents need to exhibit robustness against worst-case situations. The robust RL framework addresses this challenge via a worst-case optimization between an agent and an adversary. Previous robust RL algorithms are either sample inefficient, lack robustness guarantees, or do not scale to large problems. We propose the Robust Hallucinated Upper-Confidence RL (RH-UCRL) algorithm to provably solve this problem while attaining near-optimal sample complexity guarantees. RH-UCRL is a model-based reinforcement learning (MBRL) algorithm that effectively distinguishes between epistemic and aleatoric uncertainty and efficiently explores both the agent and adversary decision spaces during policy learning. We scale RH-UCRL to complex tasks via neural networks ensemble models as well as neural network policies. Experimentally, we demonstrate that RH-UCRL outperforms other robust deep RL algorithms in a variety of adversarial environments.

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arXiv2021

Safe and Efficient Model-free Adaptive Control via Bayesian Optimization

Adaptive control approaches yield high-performance controllers when a precise system model or suitable parametrizations of the controller are available. Existing data-driven approaches for adaptive control mostly augment standard model-based methods with additional information about uncertainties in the dynamics or about disturbances. In this work, we propose a purely data-driven, model-free approach for adaptive control. Tuning low-level controllers based solely on system data raises concerns on the underlying algorithm safety and computational performance. Thus, our approach builds on GoOSE, an algorithm for safe and sample-efficient Bayesian optimization. We introduce several computational and algorithmic modifications in GoOSE that enable its practical use on a rotational motion system. We numerically demonstrate for several types of disturbances that our approach is sample efficient, outperforms constrained Bayesian optimization in terms of safety, and achieves the performance optima computed by grid evaluation. We further demonstrate the proposed adaptive control approach experimentally on a rotational motion system.

eess.SY↗

arXiv2021

Gradient Estimation with Stochastic Softmax Tricks

The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalize the Gumbel-Softmax trick to combinatorial spaces. Our framework is a unified perspective on existing relaxed estimators for perturbation models, and it contains many novel relaxations. We design structured relaxations for subset selection, spanning trees, arborescences, and others. When compared to less structured baselines, we find that stochastic softmax tricks can be used to train latent variable models that perform better and discover more latent structure.

stat.ML↗

arXiv2021

Logistic Q-Learning

We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The method is closely related to the classic Relative Entropy Policy Search (REPS) algorithm of Peters et al. (2010), with the key difference that our method introduces a Q-function that enables efficient exact model-free implementation. The main feature of our algorithm (called QREPS) is a convex loss function for policy evaluation that serves as a theoretically sound alternative to the widely used squared Bellman error. We provide a practical saddle-point optimization method for minimizing this loss function and provide an error-propagation analysis that relates the quality of the individual updates to the performance of the output policy. Finally, we demonstrate the effectiveness of our method on a range of benchmark problems.

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arXiv2021

Safe non-smooth black-box optimization with application to policy search

For safety-critical black-box optimization tasks, observations of the constraints and the objective are often noisy and available only for the feasible points. We propose an approach based on log barriers to find a local solution of a non-convex non-smooth black-box optimization problem $\min f^0(x)$ subject to $f^i(x)\leq 0,~ i = 1,\ldots, m$, at the same time, guaranteeing constraint satisfaction while learning an optimal solution with high probability. Our proposed algorithm exploits noisy observations to iteratively improve on an initial safe point until convergence. We derive the convergence rate and prove safety of our algorithm. We demonstrate its performance in an application to an iterative control design problem.

math.OC↗

arXiv2021

Risk-Averse Offline Reinforcement Learning

Training Reinforcement Learning (RL) agents in high-stakes applications might be too prohibitive due to the risk associated to exploration. Thus, the agent can only use data previously collected by safe policies. While previous work considers optimizing the average performance using offline data, we focus on optimizing a risk-averse criteria, namely the CVaR. In particular, we present the Offline Risk-Averse Actor-Critic (O-RAAC), a model-free RL algorithm that is able to learn risk-averse policies in a fully offline setting. We show that O-RAAC learns policies with higher CVaR than risk-neutral approaches in different robot control tasks. Furthermore, considering risk-averse criteria guarantees distributional robustness of the average performance with respect to particular distribution shifts. We demonstrate empirically that in the presence of natural distribution-shifts, O-RAAC learns policies with good average performance.

cs.LG↗

arXiv2021

Safe Reinforcement Learning via Curriculum Induction

In safety-critical applications, autonomous agents may need to learn in an environment where mistakes can be very costly. In such settings, the agent needs to behave safely not only after but also while learning. To achieve this, existing safe reinforcement learning methods make an agent rely on priors that let it avoid dangerous situations during exploration with high probability, but both the probabilistic guarantees and the smoothness assumptions inherent in the priors are not viable in many scenarios of interest such as autonomous driving. This paper presents an alternative approach inspired by human teaching, where an agent learns under the supervision of an automatic instructor that saves the agent from violating constraints during learning. In this model, we introduce the monitor that neither needs to know how to do well at the task the agent is learning nor needs to know how the environment works. Instead, it has a library of reset controllers that it activates when the agent starts behaving dangerously, preventing it from doing damage. Crucially, the choices of which reset controller to apply in which situation affect the speed of agent learning. Based on observing agents' progress, the teacher itself learns a policy for choosing the reset controllers, a curriculum, to optimize the agent's final policy reward. Our experiments use this framework in two environments to induce curricula for safe and efficient learning.

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arXiv2021

Efficient Pure Exploration for Combinatorial Bandits with Semi-Bandit Feedback

Combinatorial bandits with semi-bandit feedback generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. The action set satisfies a given structure such as forming a base of a matroid or a path in a graph. We focus on the pure-exploration problem of identifying the best arm with fixed confidence, as well as a more general setting, where the structure of the answer set differs from the one of the action set. Using the recently popularized game framework, we interpret this problem as a sequential zero-sum game and develop a CombGame meta-algorithm whose instances are asymptotically optimal algorithms with finite time guarantees. In addition to comparing two families of learners to instantiate our meta-algorithm, the main contribution of our work is a specific oracle efficient instance for best-arm identification with combinatorial actions. Based on a projection-free online learning algorithm for convex polytopes, it is the first computationally efficient algorithm which is asymptotically optimal and has competitive empirical performance.

stat.ML↗

arXiv2020

Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning

Model-based reinforcement learning algorithms with probabilistic dynamical models are amongst the most data-efficient learning methods. This is often attributed to their ability to distinguish between epistemic and aleatoric uncertainty. However, while most algorithms distinguish these two uncertainties for learning the model, they ignore it when optimizing the policy, which leads to greedy and insufficient exploration. At the same time, there are no practical solvers for optimistic exploration algorithms. In this paper, we propose a practical optimistic exploration algorithm (H-UCRL). H-UCRL reparameterizes the set of plausible models and hallucinates control directly on the epistemic uncertainty. By augmenting the input space with the hallucinated inputs, H-UCRL can be solved using standard greedy planners. Furthermore, we analyze H-UCRL and construct a general regret bound for well-calibrated models, which is provably sublinear in the case of Gaussian Process models. Based on this theoretical foundation, we show how optimistic exploration can be easily combined with state-of-the-art reinforcement learning algorithms and different probabilistic models. Our experiments demonstrate that optimistic exploration significantly speeds-up learning when there are penalties on actions, a setting that is notoriously difficult for existing model-based reinforcement learning algorithms.

cs.LG↗

arXiv2020

Learning Stabilizing Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory

The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR). We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set. We further show that the feasibility conditions of the proposed SDPs are \emph{equivalent}. Using the derived robust controller syntheses, we propose an efficient data dependent algorithm -- \textsc{eXploration} -- that with high probability quickly identifies a stabilizing controller. Our approach can be used to initialize existing algorithms that require a stabilizing controller as an input while adding constant to the regret. We further propose different heuristics which empirically reduce the number of steps taken by \textsc{eXploration} and reduce the suffered cost while searching for a stabilizing controller.

eess.SY↗

arXiv2020

Adaptive Sampling for Stochastic Risk-Averse Learning

In high-stakes machine learning applications, it is crucial to not only perform well on average, but also when restricted to difficult examples. To address this, we consider the problem of training models in a risk-averse manner. We propose an adaptive sampling algorithm for stochastically optimizing the Conditional Value-at-Risk (CVaR) of a loss distribution, which measures its performance on the $α$ fraction of most difficult examples. We use a distributionally robust formulation of the CVaR to phrase the problem as a zero-sum game between two players, and solve it efficiently using regret minimization. Our approach relies on sampling from structured Determinantal Point Processes (DPPs), which enables scaling it to large data sets. Finally, we empirically demonstrate its effectiveness on large-scale convex and non-convex learning tasks.

cs.LG↗

arXiv2020

Stochastic Linear Bandits Robust to Adversarial Attacks

We consider a stochastic linear bandit problem in which the rewards are not only subject to random noise, but also adversarial attacks subject to a suitable budget $C$ (i.e., an upper bound on the sum of corruption magnitudes across the time horizon). We provide two variants of a Robust Phased Elimination algorithm, one that knows $C$ and one that does not. Both variants are shown to attain near-optimal regret in the non-corrupted case $C = 0$, while incurring additional additive terms respectively having a linear and quadratic dependency on $C$ in general. We present algorithm independent lower bounds showing that these additive terms are near-optimal. In addition, in a contextual setting, we revisit a setup of diverse contexts, and show that a simple greedy algorithm is provably robust with a near-optimal additive regret term, despite performing no explicit exploration and not knowing $C$.

stat.ML↗

arXiv2020

Coresets via Bilevel Optimization for Continual Learning and Streaming

Coresets are small data summaries that are sufficient for model training. They can be maintained online, enabling efficient handling of large data streams under resource constraints. However, existing constructions are limited to simple models such as k-means and logistic regression. In this work, we propose a novel coreset construction via cardinality-constrained bilevel optimization. We show how our framework can efficiently generate coresets for deep neural networks, and demonstrate its empirical benefits in continual learning and in streaming settings.

cs.LG↗

arXiv2020

Semi-supervised Batch Active Learning via Bilevel Optimization

Active learning is an effective technique for reducing the labeling cost by improving data efficiency. In this work, we propose a novel batch acquisition strategy for active learning in the setting where the model training is performed in a semi-supervised manner. We formulate our approach as a data summarization problem via bilevel optimization, where the queried batch consists of the points that best summarize the unlabeled data pool. We show that our method is highly effective in keyword detection tasks in the regime when only few labeled samples are available.

cs.LG↗

arXiv2020

Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator

Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple function evaluations, or use learned, input-dependent baselines. Thus, there is a need for estimators that require minimal tuning, are computationally cheap, and have low mean squared error. In this paper, we show that the variance of the straight-through variant of the popular Gumbel-Softmax estimator can be reduced through Rao-Blackwellization without increasing the number of function evaluations. This provably reduces the mean squared error. We empirically demonstrate that this leads to variance reduction, faster convergence, and generally improved performance in two unsupervised latent variable models.

stat.ML↗

arXiv2020

Mixed-Variable Bayesian Optimization

The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering. In Bayesian optimization (BO), special cases of this problem that consider fully continuous or fully discrete domains have been widely studied. However, few methods exist for mixed-variable domains and none of them can handle discrete constraints that arise in many real-world applications. In this paper, we introduce MiVaBo, a novel BO algorithm for the efficient optimization of mixed-variable functions combining a linear surrogate model based on expressive feature representations with Thompson sampling. We propose an effective method to optimize its acquisition function, a challenging problem for mixed-variable domains, making MiVaBo the first BO method that can handle complex constraints over the discrete variables. Moreover, we provide the first convergence analysis of a mixed-variable BO algorithm. Finally, we show that MiVaBo is significantly more sample efficient than state-of-the-art mixed-variable BO algorithms on several hyperparameter tuning tasks, including the tuning of deep generative models.

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arXiv2020

A domain agnostic measure for monitoring and evaluating GANs

Generative Adversarial Networks (GANs) have shown remarkable results in modeling complex distributions, but their evaluation remains an unsettled issue. Evaluations are essential for: (i) relative assessment of different models and (ii) monitoring the progress of a single model throughout training. The latter cannot be determined by simply inspecting the generator and discriminator loss curves as they behave non-intuitively. We leverage the notion of duality gap from game theory to propose a measure that addresses both (i) and (ii) at a low computational cost. Extensive experiments show the effectiveness of this measure to rank different GAN models and capture the typical GAN failure scenarios, including mode collapse and non-convergent behaviours. This evaluation metric also provides meaningful monitoring on the progression of the loss during training. It highly correlates with FID on natural image datasets, and with domain specific scores for text, sound and cosmology data where FID is not directly suitable. In particular, our proposed metric requires no labels or a pretrained classifier, making it domain agnostic.

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