Storchastic: A Framework for General Stochastic Automatic Differentiation (2104.00428v3)

Abstract: Modelers use automatic differentiation (AD) of computation graphs to implement complex Deep Learning models without defining gradient computations. Stochastic AD extends AD to stochastic computation graphs with sampling steps, which arise when modelers handle the intractable expectations common in Reinforcement Learning and Variational Inference. However, current methods for stochastic AD are limited: They are either only applicable to continuous random variables and differentiable functions, or can only use simple but high variance score-function estimators. To overcome these limitations, we introduce Storchastic, a new framework for AD of stochastic computation graphs. Storchastic allows the modeler to choose from a wide variety of gradient estimation methods at each sampling step, to optimally reduce the variance of the gradient estimates. Furthermore, Storchastic is provably unbiased for estimation of any-order gradients, and generalizes variance reduction techniques to higher-order gradient estimates. Finally, we implement Storchastic as a PyTorch library at https://github.com/HEmile/storchastic.

• The paper provides a framework that enables unbiased gradient estimates of any order in stochastic computation graphs, overcoming limitations of traditional AD.
• It decomposes gradient estimation into a proposal distribution, weighting function, gradient function, and control variate to effectively reduce variance.
• Numerical experiments with a discrete variational autoencoder demonstrate the framework’s robustness and practical benefits for advanced AI applications.

An Analysis of "Storchastic: A Framework for General Stochastic Automatic Differentiation"

The paper "Storchastic: A Framework for General Stochastic Automatic Differentiation" introduces a new framework designed to extend the automatic differentiation (AD) capabilities commonly used in deep learning to stochastic computation graphs (SCGs). This framework, termed "Storchastic," is noteworthy for its ability to deliver unbiased estimates of any-order derivatives within SCGs. Here, we delve into the construction of this framework, its methodological contributions, and its implications for future AI developments.

Automatic differentiation has fundamentally empowered the deep learning community by abstracting away the complexities of gradient computation in deterministic computation graphs. However, many modern applications, notably those in reinforcement learning and variational inference, involve intractable expectations over random variables. This necessitates extending AD frameworks to accommodate stochastic computation, which involves stochastic computation graphs where nodes represent random variables or deterministic functions of other nodes. The intricacy arises at sampling steps within these SCGs, which conventional AD methods inadequately support.

Framework and Contributions

Storchastic presents a structured attempt to facilitate gradient estimation in SCGs, addressing limitations typical in existing methods. It incorporates various gradient estimation techniques to mitigate high variance, often a bottleneck when using score-based estimators naively. Its pivotal feature is a decomposition of gradient estimation into four components: a proposal distribution, weighting function, gradient function, and control variate. This functionality allows modelers to selectively employ different gradient estimation strategies at each node, catering to specific characteristics of their problems.

The paper provides a formalization of these components and establishes conditions (Theorem 1) under which the Storchastic framework guarantees unbiased gradient estimates of any order. The employment of the MagicBox operator ensures that stochastic nodes properly integrate control variates, extending variance reduction techniques to higher-order derivatives—an advancement previously unattainable in generalized settings.

Numerical Results and Claims

The implemented PyTorch library, available on GitHub, demonstrates Storchastic’s effectiveness through numerical experiments involving a discrete variational autoencoder. The application of various gradient estimators, such as score-function methods with leave-one-out baselines and RELAX, affirms the framework's flexibility and robustness against high-variance gradient estimates. These methods highlight Storchastic's superior performance in scenarios otherwise challenged by the instability and convergence issues of traditional approaches.

Implications for AI Research

Practically, the Storchastic framework significantly expands the toolkit available to deep learning practitioners, facilitating the adoption of sophisticated models necessitating stochastic modeling, like reinforcement learning with high-dimensional action spaces or latent variable models utilizing variational inference. Theoretically, the potential to generalize variance reduction to any-order derivatives could reshape optimization strategies within AI, particularly where gradient-based approaches form the backbone, such as meta-learning.

Importantly, the paper highlights future directions, including potential bias trade-offs by incorporating biased methods and further variance analysis. Such inquiries could unveil additional layers of optimization, further enhancing the efficacy and efficiency of AI training paradigms.

In conclusion, by providing a comprehensive framework for stochastic gradient estimation, Storchastic addresses existing methodological gaps and propounds substantial theoretical advancements in automatic differentiation of stochastic computation graphs. As AI research continually evolves, frameworks like Storchastic play a crucial role in overcoming inherent computational challenges, thus expanding the horizons of machine learning and artificial intelligence applications.