arXiv subjects

Andreas Krause

Publications and source records attributed to Andreas Krause.

At least 199 records · Page 11Linked to original sources

arXiv2021

Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation

We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank latent encoding, coupled with cross-approximation (CA) to learn the representation through a subset of the original samples. CA is an adaptive sampling algorithm that is native to tensor decompositions and avoids working with the full high-resolution data explicitly. Instead, it actively selects local representative samples that we fetch out-of-core and on-demand. The required number of samples grows only logarithmically with the size of the input. Our implicit representation of the tensor in the network enables processing large grids that could not be otherwise tractable in their uncompressed form. The proposed approach is particularly useful for large-scale multidimensional grid data (e.g., 3D tomography), and for tasks that require context over a large receptive field (e.g., predicting the medical condition of entire organs). The code is available at https://github.com/aelphy/c-pic.

cs.CV↗

arXiv2021

Misspecified Gaussian Process Bandit Optimization

We consider the problem of optimizing a black-box function based on noisy bandit feedback. Kernelized bandit algorithms have shown strong empirical and theoretical performance for this problem. They heavily rely on the assumption that the model is well-specified, however, and can fail without it. Instead, we introduce a \emph{misspecified} kernelized bandit setting where the unknown function can be $ε$--uniformly approximated by a function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS). We design efficient and practical algorithms whose performance degrades minimally in the presence of model misspecification. Specifically, we present two algorithms based on Gaussian process (GP) methods: an optimistic EC-GP-UCB algorithm that requires knowing the misspecification error, and Phased GP Uncertainty Sampling, an elimination-type algorithm that can adapt to unknown model misspecification. We provide upper bounds on their cumulative regret in terms of $ε$, the time horizon, and the underlying kernel, and we show that our algorithm achieves optimal dependence on $ε$ with no prior knowledge of misspecification. In addition, in a stochastic contextual setting, we show that EC-GP-UCB can be effectively combined with the regret bound balancing strategy and attain similar regret bounds despite not knowing $ε$.

cs.LG↗

arXiv2021

Risk-averse Heteroscedastic Bayesian Optimization

Many black-box optimization tasks arising in high-stakes applications require risk-averse decisions. The standard Bayesian optimization (BO) paradigm, however, optimizes the expected value only. We generalize BO to trade mean and input-dependent variance of the objective, both of which we assume to be unknown a priori. In particular, we propose a novel risk-averse heteroscedastic Bayesian optimization algorithm (RAHBO) that aims to identify a solution with high return and low noise variance, while learning the noise distribution on the fly. To this end, we model both expectation and variance as (unknown) RKHS functions, and propose a novel risk-aware acquisition function. We bound the regret for our approach and provide a robust rule to report the final decision point for applications where only a single solution must be identified. We demonstrate the effectiveness of RAHBO on synthetic benchmark functions and hyperparameter tuning tasks.

cs.LG↗

arXiv2021

Robust Generalization despite Distribution Shift via Minimum Discriminating Information

Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the shifted test distribution. We employ the principle of minimum discriminating information to embed the available prior knowledge, and use distributionally robust optimization to account for uncertainty due to the limited samples. By leveraging large deviation results, we obtain explicit generalization bounds with respect to the unknown shifted distribution. Lastly, we demonstrate the versatility of our framework by demonstrating it on two rather distinct applications: (1) training classifiers on systematically biased data and (2) off-policy evaluation in Markov Decision Processes.

cs.LG↗

arXiv2021

Hierarchical Skills for Efficient Exploration

In reinforcement learning, pre-trained low-level skills have the potential to greatly facilitate exploration. However, prior knowledge of the downstream task is required to strike the right balance between generality (fine-grained control) and specificity (faster learning) in skill design. In previous work on continuous control, the sensitivity of methods to this trade-off has not been addressed explicitly, as locomotion provides a suitable prior for navigation tasks, which have been of foremost interest. In this work, we analyze this trade-off for low-level policy pre-training with a new benchmark suite of diverse, sparse-reward tasks for bipedal robots. We alleviate the need for prior knowledge by proposing a hierarchical skill learning framework that acquires skills of varying complexity in an unsupervised manner. For utilization on downstream tasks, we present a three-layered hierarchical learning algorithm to automatically trade off between general and specific skills as required by the respective task. In our experiments, we show that our approach performs this trade-off effectively and achieves better results than current state-of-the-art methods for end- to-end hierarchical reinforcement learning and unsupervised skill discovery. Code and videos are available at https://facebookresearch.github.io/hsd3 .

cs.LG↗

arXiv2021

Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.

cs.LG↗

arXiv2021

Data Summarization via Bilevel Optimization

The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a simple yet powerful approach is to operate on small subsets of the data. Coresets are weighted subsets of the data that provide approximation guarantees for the optimization objective. However, existing coreset constructions are highly model-specific and are limited to simple models such as linear regression, logistic regression, and $k$-means. In this work, we propose a generic coreset construction framework that formulates the coreset selection as a cardinality-constrained bilevel optimization problem. In contrast to existing approaches, our framework does not require model-specific adaptations and applies to any twice differentiable model, including neural networks. We show the effectiveness of our framework for a wide range of models in various settings, including training non-convex models online and batch active learning.

cs.LG↗

arXiv2021

Fast Projection Onto Convex Smooth Constraints

The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on projection problems where the constraints are smooth and the number of constraints is significantly smaller than the dimension. The runtime of existing approaches to solving such problems is either cubic in the dimension or polynomial in the inverse of the target accuracy. Conversely, we propose a simple and efficient primal-dual approach, with a runtime that scales only linearly with the dimension, and only logarithmically in the inverse of the target accuracy. We empirically demonstrate its performance, and compare it with standard baselines.

math.OC↗

arXiv2021

Incentive-Compatible Forecasting Competitions

We initiate the study of incentive-compatible forecasting competitions in which multiple forecasters make predictions about one or more events and compete for a single prize. We have two objectives: (1) to incentivize forecasters to report truthfully and (2) to award the prize to the most accurate forecaster. Proper scoring rules incentivize truthful reporting if all forecasters are paid according to their scores. However, incentives become distorted if only the best-scoring forecaster wins a prize, since forecasters can often increase their probability of having the highest score by reporting more extreme beliefs. In this paper, we introduce two novel forecasting competition mechanisms. Our first mechanism is incentive compatible and guaranteed to select the most accurate forecaster with probability higher than any other forecaster. Moreover, we show that in the standard single-event, two-forecaster setting and under mild technical conditions, no other incentive-compatible mechanism selects the most accurate forecaster with higher probability. Our second mechanism is incentive compatible when forecasters' beliefs are such that information about one event does not lead to belief updates on other events, and it selects the best forecaster with probability approaching 1 as the number of events grows. Our notion of incentive compatibility is more general than previous definitions of dominant strategy incentive compatibility in that it allows for reports to be correlated with the event outcomes. Moreover, our mechanisms are easy to implement and can be generalized to the related problems of outputting a ranking over forecasters and hiring a forecaster with high accuracy on future events.

cs.GT↗

arXiv2021

Contextual Games: Multi-Agent Learning with Side Information

We formulate the novel class of contextual games, a type of repeated games driven by contextual information at each round. By means of kernel-based regularity assumptions, we model the correlation between different contexts and game outcomes and propose a novel online (meta) algorithm that exploits such correlations to minimize the contextual regret of individual players. We define game-theoretic notions of contextual Coarse Correlated Equilibria (c-CCE) and optimal contextual welfare for this new class of games and show that c-CCEs and optimal welfare can be approached whenever players' contextual regrets vanish. Finally, we empirically validate our results in a traffic routing experiment, where our algorithm leads to better performance and higher welfare compared to baselines that do not exploit the available contextual information or the correlations present in the game.

cs.GT↗

arXiv2021

PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees

Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.

stat.ML↗

arXiv2021

PopSkipJump: Decision-Based Attack for Probabilistic Classifiers

Most current classifiers are vulnerable to adversarial examples, small input perturbations that change the classification output. Many existing attack algorithms cover various settings, from white-box to black-box classifiers, but typically assume that the answers are deterministic and often fail when they are not. We therefore propose a new adversarial decision-based attack specifically designed for classifiers with probabilistic outputs. It is based on the HopSkipJump attack by Chen et al. (2019, arXiv:1904.02144v5 ), a strong and query efficient decision-based attack originally designed for deterministic classifiers. Our P(robabilisticH)opSkipJump attack adapts its amount of queries to maintain HopSkipJump's original output quality across various noise levels, while converging to its query efficiency as the noise level decreases. We test our attack on various noise models, including state-of-the-art off-the-shelf randomized defenses, and show that they offer almost no extra robustness to decision-based attacks. Code is available at https://github.com/cjsg/PopSkipJump .

cs.LG↗

arXiv2021

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.

stat.ML↗

arXiv2021

Learning Graph Models for Retrosynthesis Prediction

Retrosynthesis prediction is a fundamental problem in organic synthesis, where the task is to identify precursor molecules that can be used to synthesize a target molecule. A key consideration in building neural models for this task is aligning model design with strategies adopted by chemists. Building on this viewpoint, this paper introduces a graph-based approach that capitalizes on the idea that the graph topology of precursor molecules is largely unaltered during a chemical reaction. The model first predicts the set of graph edits transforming the target into incomplete molecules called synthons. Next, the model learns to expand synthons into complete molecules by attaching relevant leaving groups. This decomposition simplifies the architecture, making its predictions more interpretable, and also amenable to manual correction. Our model achieves a top-1 accuracy of $53.7\%$, outperforming previous template-free and semi-template-based methods.

cs.LG↗

arXiv2021

Addressing the Long-term Impact of ML Decisions via Policy Regret

Machine Learning (ML) increasingly informs the allocation of opportunities to individuals and communities in areas such as lending, education, employment, and beyond. Such decisions often impact their subjects' future characteristics and capabilities in an a priori unknown fashion. The decision-maker, therefore, faces exploration-exploitation dilemmas akin to those in multi-armed bandits. Following prior work, we model communities as arms. To capture the long-term effects of ML-based allocation decisions, we study a setting in which the reward from each arm evolves every time the decision-maker pulls that arm. We focus on reward functions that are initially increasing in the number of pulls but may become (and remain) decreasing after a certain point. We argue that an acceptable sequential allocation of opportunities must take an arm's potential for growth into account. We capture these considerations through the notion of policy regret, a much stronger notion than the often-studied external regret, and present an algorithm with provably sub-linear policy regret for sufficiently long time horizons. We empirically compare our algorithm with several baselines and find that it consistently outperforms them, in particular for long time horizons.

cs.LG↗

arXiv2021

A note on the CAPM with endogenously consistent market returns

I demonstrate that with the market return determined by the equilibrium returns of the CAPM, expected returns of an asset are affected by the risks of all assets jointly. Another implication is that the range of feasible market returns will be limited and dependent on the distribution of weights in the market portfolio. A large and well diversified market with no dominating asset will only return zero while a market dominated by a small number of assets will only return the risk-free rate. In the limiting case of atomistic assets, we recover the properties of the standard CAPM.

q-fin.GN↗

arXiv2021

A Human-in-the-loop Framework to Construct Context-aware Mathematical Notions of Outcome Fairness

Existing mathematical notions of fairness fail to account for the context of decision-making. We argue that moral consideration of contextual factors is an inherently human task. So we present a framework to learn context-aware mathematical formulations of fairness by eliciting people's situated fairness assessments. Our family of fairness notions corresponds to a new interpretation of economic models of Equality of Opportunity (EOP), and it includes most existing notions of fairness as special cases. Our human-in-the-loop approach is designed to learn the appropriate parameters of the EOP family by utilizing human responses to pair-wise questions about decision subjects' circumstance and deservingness, and the harm/benefit imposed on them. We illustrate our framework in a hypothetical criminal risk assessment scenario by conducting a series of human-subject experiments on Amazon Mechanical Turk. Our work takes an important initial step toward empowering stakeholders to have a voice in the formulation of fairness for Machine Learning.

cs.AI↗

arXiv2021

Online Active Model Selection for Pre-trained Classifiers

Given $k$ pre-trained classifiers and a stream of unlabeled data examples, how can we actively decide when to query a label so that we can distinguish the best model from the rest while making a small number of queries? Answering this question has a profound impact on a range of practical scenarios. In this work, we design an online selective sampling approach that actively selects informative examples to label and outputs the best model with high probability at any round. Our algorithm can be used for online prediction tasks for both adversarial and stochastic streams. We establish several theoretical guarantees for our algorithm and extensively demonstrate its effectiveness in our experimental studies.

cs.LG↗