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Jonas Rothfuss

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11 papers

2 author rows

IROS Conference 2024 Conference Paper

Bridging the Sim-to-Real Gap with Bayesian Inference

Jonas Rothfuss
Bhavya Sukhija
Lenart Treven
Florian Dörfler
Stelian Coros
Andreas Krause 0001

We present Sim-FSVGD for learning robot dynamics from data. As opposed to traditional methods, Sim-FSVGD leverages low-fidelity physical priors, e. g. , in the form of simulators, to regularize the training of neural network models. While learning accurate dynamics already in the low data regime, Sim-FSVGD scales and excels also when more data is available. We empirically show that learning with implicit physical priors results in accurate mean model estimation as well as precise uncertainty quantification. We demonstrate the effectiveness of Sim-FSVGD in bridging the sim-to-real gap on a high-performance RC racecar system. Using model-based RL, we demonstrate a highly dynamic parking maneuver with drifting, using less than half the data compared to the state of the art.

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UAI Conference 2023 Conference Paper

Hallucinated adversarial control for conservative offline policy evaluation

Jonas Rothfuss
Bhavya Sukhija
Tobias Birchler
Parnian Kassraie
Andreas Krause 0001

We study the problem of conservative off-policy evaluation (COPE) where given an offline dataset of environment interactions, collected by other agents, we seek to obtain a (tight) lower bound on a policy’s performance. This is crucial when deciding whether a given policy satisfies certain minimal performance/safety criteria before it can be deployed in the real world. To this end, we introduce HAMBO, which builds on an uncertainty-aware learned model of the transition dynamics. To form a conservative estimate of the policy’s performance, HAMBO hallucinates worst-case trajectories that the policy may take, within the margin of the models’ epistemic confidence regions. We prove that the resulting COPE estimates are valid lower bounds, and, under regularity conditions, show their convergence to the true expected return. Finally, we discuss scalable variants of our approach based on Bayesian Neural Networks and empirically demonstrate that they yield reliable and tight lower bounds in various continuous control environments.

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JMLR Journal 2023 Journal Article

Instance-Dependent Generalization Bounds via Optimal Transport

Songyan Hou
Parnian Kassraie
Anastasis Kratsios
Andreas Krause
Jonas Rothfuss

Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. Since such bounds often hold uniformly over all parameters, they suffer from over-parametrization and fail to account for the strong inductive bias of initialization and stochastic gradient descent. As an alternative, we propose a novel optimal transport interpretation of the generalization problem. This allows us to derive instance-dependent generalization bounds that depend on the local Lipschitz regularity of the learned prediction function in the data space. Therefore, our bounds are agnostic to the parametrization of the model and work well when the number of training samples is much smaller than the number of parameters. With small modifications, our approach yields accelerated rates for data on low-dimensional manifolds and guarantees under distribution shifts. We empirically analyze our generalization bounds for neural networks, showing that the bound values are meaningful and capture the effect of popular regularization methods during training. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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UAI Conference 2023 Conference Paper

Lifelong bandit optimization: no prior and no regret

Felix Schur
Parnian Kassraie
Jonas Rothfuss
Andreas Krause 0001

Machine learning algorithms are often repeatedly. applied to problems with similar structure over and over again. We focus on solving a sequence of bandit optimization tasks and develop LIBO, an algorithm which adapts to the environment by learning from past experience and becomes more sample-efficient in the process. We assume a kernelized structure where the kernel is unknown but shared across all tasks. LIBO sequentially meta-learns a kernel that approximates the true kernel and solves the incoming tasks with the latest kernel estimate. Our algorithm can be paired with any kernelized or linear bandit algorithm and guarantees oracle optimal performance, meaning that as more tasks are solved, the regret of LIBO on each task converges to the regret of the bandit algorithm with oracle knowledge of the true kernel. Naturally, if paired with a sublinear bandit algorithm, LIBO yields a sublinear lifelong regret. We also show that direct access to the data from each task is not necessary for attaining sublinear regret. We propose F-LIBO, which solves the lifelong problem in a federated manner.

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ICLR Conference 2023 Conference Paper

MARS: Meta-learning as Score Matching in the Function Space

Krunoslav Lehman Pavasovic
Jonas Rothfuss
Andreas Krause 0001

Meta-learning aims to extract useful inductive biases from a set of related datasets. In Bayesian meta-learning, this is typically achieved by constructing a prior distribution over neural network parameters. However, specifying families of computationally viable prior distributions over the high-dimensional neural network parameters is difficult. As a result, existing approaches resort to meta-learning restrictive diagonal Gaussian priors, severely limiting their expressiveness and performance. To circumvent these issues, we approach meta-learning through the lens of functional Bayesian neural network inference which views the prior as a stochastic process and performs inference in the function space. Specifically, we view the meta-training tasks as samples from the data-generating process and formalize meta-learning as empirically estimating the law of this stochastic process. Our approach can seamlessly acquire and represent complex prior knowledge by meta-learning the score function of the data-generating process marginals instead of parameter space priors. In a comprehensive benchmark, we demonstrate that our method achieves state-of-the-art performance in terms of predictive accuracy and substantial improvements in the quality of uncertainty estimates.

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JMLR Journal 2023 Journal Article

Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practice

Jonas Rothfuss
Martin Josifoski
Vincent Fortuin
Andreas Krause

Meta-Learning aims to speed up the learning process on new tasks by acquiring useful inductive biases from datasets of related learning tasks. While, in practice, the number of related tasks available is often small, most of the existing approaches assume an abundance of tasks; making them unrealistic and prone to overfitting. A central question in the meta-learning literature is how to regularize to ensure generalization to unseen tasks. In this work, we provide a theoretical analysis using the PAC-Bayesian theory and present a generalization bound for meta-learning, which was first derived by Rothfuss et al. (2021). Crucially, the bound allows us to derive the closed form of the optimal hyper-posterior, referred to as PACOH, which leads to the best performance guarantees. We provide a theoretical analysis and empirical case study under which conditions and to what extent these guarantees for meta-learning improve upon PAC-Bayesian per-task learning bounds. The closed-form PACOH inspires a practical meta-learning approach that avoids the reliance on bi-level optimization, giving rise to a stochastic optimization problem that is amenable to standard variational methods that scale well. Our experiments show that, when instantiating the PACOH with Gaussian processes and Bayesian Neural Networks models, the resulting methods are more scalable, and yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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NeurIPS Conference 2022 Conference Paper

Amortized Inference for Causal Structure Learning

Lars Lorch
Scott Sussex
Jonas Rothfuss
Andreas Krause
Bernhard Schölkopf

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https: //github. com/larslorch/avici

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ICML Conference 2022 Conference Paper

Meta-Learning Hypothesis Spaces for Sequential Decision-making

Parnian Kassraie
Jonas Rothfuss
Andreas Krause 0001

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on prior assumptions on the hypothesis space, e. g. , the known kernel of a Reproducing Kernel Hilbert Space (RKHS). Hand-designing such kernels is error prone, and misspecification may lead to poor or unsafe performance. In this work, we propose to meta-learn a kernel from offline data (Meta-KeL). For the case where the unknown kernel is a combination of known base kernels, we develop an estimator based on structured sparsity. Under mild conditions, we guarantee that our estimated RKHS yields valid confidence sets that, with increasing amounts of offline data, become as tight as those given the true unknown kernel. We demonstrate our approach on the kernelized bandits problem (a. k. a. Bayesian optimization), where we establish regret bounds competitive with those given the true kernel. We also empirically evaluate the effectiveness of our approach on a Bayesian optimization task.

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NeurIPS Conference 2021 Conference Paper

DiBS: Differentiable Bayesian Structure Learning

Lars Lorch
Jonas Rothfuss
Bernhard Schölkopf
Andreas Krause

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty---a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our formulation directly applicable to posterior inference of nonstandard Bayesian network models, e. g. , with nonlinear dependencies encoded by neural networks. Using DiBS, we devise an efficient, general purpose variational inference method for approximating distributions over structural models. In evaluations on simulated and real-world data, our method significantly outperforms related approaches to joint posterior inference.

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NeurIPS Conference 2021 Conference Paper

Meta-Learning Reliable Priors in the Function Space

Jonas Rothfuss
Dominique Heyn
jinfan Chen
Andreas Krause

Meta-Learning promises to enable more data-efficient inference by harnessing previous experience from related learning tasks. While existing meta-learning methods help us to improve the accuracy of our predictions in face of data scarcity, they fail to supply reliable uncertainty estimates, often being grossly overconfident in their predictions. Addressing these shortcomings, we introduce a novel meta-learning framework, called F-PACOH, that treats meta-learned priors as stochastic processes and performs meta-level regularization directly in the function space. This allows us to directly steer the probabilistic predictions of the meta-learner towards high epistemic uncertainty in regions of insufficient meta-training data and, thus, obtain well-calibrated uncertainty estimates. Finally, we showcase how our approach can be integrated with sequential decision making, where reliable uncertainty quantification is imperative. In our benchmark study on meta-learning for Bayesian Optimization (BO), F-PACOH significantly outperforms all other meta-learners and standard baselines. Even in a challenging lifelong BO setting, where optimization tasks arrive one at a time and the meta-learner needs to build up informative prior knowledge incrementally, our proposed method demonstrates strong positive transfer.

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ICML Conference 2021 Conference Paper

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

Jonas Rothfuss
Vincent Fortuin
Martin Josifoski
Andreas Krause 0001

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.

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