PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees (2002.05551v5)

Abstract: 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.

• The paper introduces a PAC-optimal meta-learning framework that leverages PAC-Bayesian bounds to counteract overfitting in limited-task scenarios.
• It employs Gaussian Processes and Bayesian Neural Networks with variational and particle-based inference for efficient stochastic optimization.
• Empirical evaluations show significant gains in predictive accuracy and uncertainty calibration, validating PACOH's real-world applicability.

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

The paper "PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees" addresses key challenges in the field of meta-learning, particularly focusing on generalization in scenarios with limited meta-training tasks. Conventional meta-learning approaches are often prone to overfitting when faced with a small number of training tasks. To counteract this, the authors employ a PAC-Bayesian theoretical framework to develop novel generalization bounds specific to meta-learning. These bounds provide the foundational basis for proposing a new class of PAC-optimal meta-learning algorithms.

Theoretical Contributions

The core theoretical contribution of this work is the derivation of PAC-Bayesian generalization bounds applicable to meta-learning, extended to include contexts with unbounded loss functions such as in regression and probabilistic inference tasks. Unlike previous approaches reliant on bounded loss functions, the authors leverage a sub-gamma assumption for loss functions, enabling more generalized applications. The paper presents a PAC-optimal hyper-posterior (PACOH) algorithm achieved through efficient stochastic optimization. This allows the method to deliver state-of-the-art generalization guarantees while avoiding the computationally prohibitive nested optimization problems characteristic of traditional PAC-Bayesian meta-learners.

Methodology

The PACOH framework is instantiated using Gaussian Processes (GPs) and Bayesian Neural Networks (BNNs) as base learners. The authors employ variational and particle-based inference methods (e.g., SVGD) to approximate the hyper-posterior distributions. This design enables straightforward integration into existing stochastic optimization workflows, thus enhancing practical scalability and efficiency. A noteworthy feature of PACOH's methodology is its principled meta-level regularization mechanism that effectively mitigates meta-overfitting, enhancing the framework's robustness even with moderately low numbers of training tasks.

Empirical Evaluations

Extensive experiments across various regression and classification environments demonstrate that PACOH consistently excels or performs competitively against established meta-learning approaches. The paper highlights significant improvements in both predictive accuracy and uncertainty calibration; the latter being essential for robust decision-making in sequential tasks such as Bayesian optimization and vaccine design studies.

In particular, empirical results underscore PACOH's capacity to generalize effectively from as few as five training tasks, positioning it as a viable option for scenarios where data acquisition is costly or impractical. Furthermore, PACOH's computational efficiency and scalability address a crucial impediment faced by prior PAC-Bayesian approaches, thereby extending its applicability to large-scale, real-world problems.

Implications and Future Work

The implications of this research are multifaceted, contributing both practical and theoretical insights to the domain of meta-learning. On a practical level, the introduction of PACOH offers a viable solution for developing meta-learners with robust generalization capabilities across diverse applications, from health care to autonomous systems. Theoretically, the paper lays the groundwork for further exploration of PAC-Bayesian approaches in meta-learning, especially in contexts requiring complex, high-dimensional posterior distributions.

Future research efforts could focus on extending the PACOH framework to accommodate recurrent models for time-series forecasting, as well as exploring adaptive mechanisms for switching priors in dynamic environments. Additionally, the integration of more expressive models, potentially through advancements in neural architecture search and hyperparameter optimization, could further elevate the performance and adaptability of PAC-optimal meta-learners.

In conclusion, this paper advances the meta-learning field through the innovative use of PAC-Bayesian theory, backed by compelling empirical evidence and potential for wide-ranging applications.