arXiv subjects

Andreas Krause

Publications and source records attributed to Andreas Krause.

At least 271 records · Page 15Linked to original sources

arXiv2019

Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computational cost are well established, a rigorous mathematical framework has been missing. We offer a novel interpretation which leads to a better understanding and improvements in state-of-the-art performance in terms of accuracy for nonlinear dynamical systems.

stat.ML↗

arXiv2019

Multi-Player Bandits: The Adversarial Case

We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by a cognitive radio networks application, we assume that players incur a loss upon colliding, and that communication between players is not possible. Existing approaches assume that the system is stationary. Yet this assumption is often violated in practice, e.g., due to signal strength fluctuations. In this work, we design the first Multi-player Bandit algorithm that provably works in arbitrarily changing environments, where the losses of the arms may even be chosen by an adversary. This resolves an open problem posed by Rosenski, Shamir, and Szlak (2016).

cs.LG↗

arXiv2019

Fairness Behind a Veil of Ignorance: A Welfare Analysis for Automated Decision Making

We draw attention to an important, yet largely overlooked aspect of evaluating fairness for automated decision making systems---namely risk and welfare considerations. Our proposed family of measures corresponds to the long-established formulations of cardinal social welfare in economics, and is justified by the Rawlsian conception of fairness behind a veil of ignorance. The convex formulation of our welfare-based measures of fairness allows us to integrate them as a constraint into any convex loss minimization pipeline. Our empirical analysis reveals interesting trade-offs between our proposal and (a) prediction accuracy, (b) group discrimination, and (c) Dwork et al.'s notion of individual fairness. Furthermore and perhaps most importantly, our work provides both heuristic justification and empirical evidence suggesting that a lower-bound on our measures often leads to bounded inequality in algorithmic outcomes; hence presenting the first computationally feasible mechanism for bounding individual-level inequality.

cs.AI↗

arXiv2018

Optimal DR-Submodular Maximization and Applications to Provable Mean Field Inference

Mean field inference in probabilistic models is generally a highly nonconvex problem. Existing optimization methods, e.g., coordinate ascent algorithms, can only generate local optima. In this work we propose provable mean filed methods for probabilistic log-submodular models and its posterior agreement (PA) with strong approximation guarantees. The main algorithmic technique is a new Double Greedy scheme, termed DR-DoubleGreedy, for continuous DR-submodular maximization with box-constraints. It is a one-pass algorithm with linear time complexity, reaching the optimal 1/2 approximation ratio, which may be of independent interest. We validate the superior performance of our algorithms against baseline algorithms on both synthetic and real-world datasets.

cs.LG↗

arXiv2018

A Moral Framework for Understanding of Fair ML through Economic Models of Equality of Opportunity

We map the recently proposed notions of algorithmic fairness to economic models of Equality of opportunity (EOP)---an extensively studied ideal of fairness in political philosophy. We formally show that through our conceptual mapping, many existing definition of algorithmic fairness, such as predictive value parity and equality of odds, can be interpreted as special cases of EOP. In this respect, our work serves as a unifying moral framework for understanding existing notions of algorithmic fairness. Most importantly, this framework allows us to explicitly spell out the moral assumptions underlying each notion of fairness, and interpret recent fairness impossibility results in a new light. Last but not least and inspired by luck egalitarian models of EOP, we propose a new family of measures for algorithmic fairness. We illustrate our proposal empirically and show that employing a measure of algorithmic (un)fairness when its underlying moral assumptions are not satisfied, can have devastating consequences for the disadvantaged group's welfare.

cs.LG↗

arXiv2018

Learning to Compensate Photovoltaic Power Fluctuations from Images of the Sky by Imitating an Optimal Policy

The energy output of photovoltaic (PV) power plants depends on the environment and thus fluctuates over time. As a result, PV power can cause instability in the power grid, in particular when increasingly used. Limiting the rate of change of the power output is a common way to mitigate these fluctuations, often with the help of large batteries. A reactive controller that uses these batteries to compensate ramps works in practice, but causes stress on the battery due to a high energy throughput. In this paper, we present a deep learning approach that uses images of the sky to compensate power fluctuations predictively and reduces battery stress. In particular, we show that the optimal control policy can be computed using information that is only available in hindsight. Based on this, we use imitation learning to train a neural network that approximates this hindsight-optimal policy, but uses only currently available sky images and sensor data. We evaluate our method on a large dataset of measurements and images from a real power plant and show that the trained policy reduces stress on the battery.

cs.LG↗

arXiv2018

Learning-based Model Predictive Control for Safe Exploration

Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that can provide provable high-probability safety guarantees. To this end, we exploit regularity assumptions on the dynamics in terms of a Gaussian process prior to construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we do not assume that model uncertainties are independent. Based on these predictions, we guarantee that trajectories satisfy safety constraints. Moreover, we use a terminal set constraint to recursively guarantee the existence of safe control actions at every iteration. In our experiments, we show that the resulting algorithm can be used to safely and efficiently explore and learn about dynamic systems.

eess.SY↗

arXiv2018

The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems

Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy typically does not yield any safety guarantees. That is, the required exploration may cause physical harm to the robot or its environment. In this paper, we present a method to learn accurate safety certificates for nonlinear, closed-loop dynamical systems. Specifically, we construct a neural network Lyapunov function and a training algorithm that adapts it to the shape of the largest safe region in the state space. The algorithm relies only on knowledge of inputs and outputs of the dynamics, rather than on any specific model structure. We demonstrate our method by learning the safe region of attraction for a simulated inverted pendulum. Furthermore, we discuss how our method can be used in safe learning algorithms together with statistical models of dynamical systems.

eess.SY↗

arXiv2018

Reinforced Imitation: Sample Efficient Deep Reinforcement Learning for Map-less Navigation by Leveraging Prior Demonstrations

This work presents a case study of a learning-based approach for target driven map-less navigation. The underlying navigation model is an end-to-end neural network which is trained using a combination of expert demonstrations, imitation learning (IL) and reinforcement learning (RL). While RL and IL suffer from a large sample complexity and the distribution mismatch problem, respectively, we show that leveraging prior expert demonstrations for pre-training can reduce the training time to reach at least the same level of performance compared to plain RL by a factor of 5. We present a thorough evaluation of different combinations of expert demonstrations, different RL algorithms and reward functions, both in simulation and on a real robotic platform. Our results show that the final model outperforms both standalone approaches in the amount of successful navigation tasks. In addition, the RL reward function can be significantly simplified when using pre-training, e.g. by using a sparse reward only. The learned navigation policy is able to generalize to unseen and real-world environments.

cs.RO↗

arXiv2018

Discrete Sampling using Semigradient-based Product Mixtures

We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and Ising models. Locally-moving Markov chain Monte Carlo algorithms, such as the Gibbs sampler, are commonly used for inference in such models, but their convergence is, at times, prohibitively slow. This is often caused by state-space bottlenecks that greatly hinder the movement of such samplers. We propose a novel sampling strategy that uses a specific mixture of product distributions to propose global moves and, thus, accelerate convergence. Furthermore, we show how to construct such a mixture using semigradient information. We illustrate the effectiveness of combining our sampler with existing ones, both theoretically on an example model, as well as practically on three models learned from real-world data sets.

cs.LG↗

arXiv2018

Differentiable Submodular Maximization

We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial nature, submodular functions can be maximized approximately with strong theoretical guarantees in polynomial time. Typically, learning the submodular function and optimization of that function are treated separately, i.e. the function is first learned using a proxy objective and subsequently maximized. In contrast, we show how to perform learning and optimization jointly. By interpreting the output of greedy maximization algorithms as distributions over sequences of items and smoothening these distributions, we obtain a differentiable objective. In this way, we can differentiate through the maximization algorithms and optimize the model to work well with the optimization algorithm. We theoretically characterize the error made by our approach, yielding insights into the tradeoff of smoothness and accuracy. We demonstrate the effectiveness of our approach for jointly learning and optimizing on synthetic maximum cut data, and on real world applications such as product recommendation and image collection summarization.

stat.ML↗

arXiv2018

Scalable k-Means Clustering via Lightweight Coresets

Coresets are compact representations of data sets such that models trained on a coreset are provably competitive with models trained on the full data set. As such, they have been successfully used to scale up clustering models to massive data sets. While existing approaches generally only allow for multiplicative approximation errors, we propose a novel notion of lightweight coresets that allows for both multiplicative and additive errors. We provide a single algorithm to construct lightweight coresets for k-means clustering as well as soft and hard Bregman clustering. The algorithm is substantially faster than existing constructions, embarrassingly parallel, and the resulting coresets are smaller. We further show that the proposed approach naturally generalizes to statistical k-means clustering and that, compared to existing results, it can be used to compute smaller summaries for empirical risk minimization. In extensive experiments, we demonstrate that the proposed algorithm outperforms existing data summarization strategies in practice.

stat.ML↗

arXiv2018

Online Variance Reduction for Stochastic Optimization

Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible remedy is to employ non-uniform importance sampling techniques, which take the structure of the dataset into account. In this work, we investigate a recently proposed setting which poses variance reduction as an online optimization problem with bandit feedback. We devise a novel and efficient algorithm for this setting that finds a sequence of importance sampling distributions competitive with the best fixed distribution in hindsight, the first result of this kind. While we present our method for sampling datapoints, it naturally extends to selecting coordinates or even blocks of thereof. Empirical validations underline the benefits of our method in several settings.

stat.ML↗

arXiv2018

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.

stat.ML↗

arXiv2018

Submodularity on Hypergraphs: From Sets to Sequences

In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a large volume of work devoted to the study of submodular functions in recent years, the vast majority of this work has been focused on algorithms that output sets, not sequences. However, in many settings, the order in which we output items can be just as important as the items themselves. To extend the notion of submodularity to sequences, we use a directed graph on the items where the edges encode the additional value of selecting items in a particular order. Existing theory is limited to the case where this underlying graph is a directed acyclic graph. In this paper, we introduce two new algorithms that provably give constant factor approximations for general graphs and hypergraphs having bounded in or out degrees. Furthermore, we show the utility of our new algorithms for real-world applications in movie recommendation, online link prediction, and the design of course sequences for MOOCs.

cs.DS↗

arXiv2018

Fake News Detection in Social Networks via Crowd Signals

Our work considers leveraging crowd signals for detecting fake news and is motivated by tools recently introduced by Facebook that enable users to flag fake news. By aggregating users' flags, our goal is to select a small subset of news every day, send them to an expert (e.g., via a third-party fact-checking organization), and stop the spread of news identified as fake by an expert. The main objective of our work is to minimize the spread of misinformation by stopping the propagation of fake news in the network. It is especially challenging to achieve this objective as it requires detecting fake news with high-confidence as quickly as possible. We show that in order to leverage users' flags efficiently, it is crucial to learn about users' flagging accuracy. We develop a novel algorithm, DETECTIVE, that performs Bayesian inference for detecting fake news and jointly learns about users' flagging accuracy over time. Our algorithm employs posterior sampling to actively trade off exploitation (selecting news that maximize the objective value at a given epoch) and exploration (selecting news that maximize the value of information towards learning about users' flagging accuracy). We demonstrate the effectiveness of our approach via extensive experiments and show the power of leveraging community signals for fake news detection.

cs.SI↗

arXiv2018

Training Gaussian Mixture Models at Scale via Coresets

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being independent of the data set size. Hence, one can harness computationally intensive algorithms to compute a good approximation on a significantly smaller data set. More importantly, such coresets can be efficiently constructed both in distributed and streaming settings and do not impose restrictions on the data generating process. Our results rely on a novel reduction of statistical estimation to problems in computational geometry and new combinatorial complexity results for mixtures of Gaussians. Empirical evaluation on several real-world datasets suggests that our coreset-based approach enables significant reduction in training-time with negligible approximation error.

stat.ML↗

arXiv2017

Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the Fly

The need for real time analysis of rapidly producing data streams (e.g., video and image streams) motivated the design of streaming algorithms that can efficiently extract and summarize useful information from massive data "on the fly". Such problems can often be reduced to maximizing a submodular set function subject to various constraints. While efficient streaming methods have been recently developed for monotone submodular maximization, in a wide range of applications, such as video summarization, the underlying utility function is non-monotone, and there are often various constraints imposed on the optimization problem to consider privacy or personalization. We develop the first efficient single pass streaming algorithm, Streaming Local Search, that for any streaming monotone submodular maximization algorithm with approximation guarantee $α$ under a collection of independence systems ${\cal I}$, provides a constant $1/\big(1+2/\sqrtα+1/α+2d(1+\sqrtα)\big)$ approximation guarantee for maximizing a non-monotone submodular function under the intersection of ${\cal I}$ and $d$ knapsack constraints. Our experiments show that for video summarization, our method runs more than 1700 times faster than previous work, while maintaining practically the same performance.

cs.DS↗