Gradient Estimation Using Stochastic Computation Graphs (1506.05254v3)

Abstract: In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external world. Estimating the gradient of this loss function, using samples, lies at the core of gradient-based learning algorithms for these problems. We introduce the formalism of stochastic computation graphs---directed acyclic graphs that include both deterministic functions and conditional probability distributions---and describe how to easily and automatically derive an unbiased estimator of the loss function's gradient. The resulting algorithm for computing the gradient estimator is a simple modification of the standard backpropagation algorithm. The generic scheme we propose unifies estimators derived in variety of prior work, along with variance-reduction techniques therein. It could assist researchers in developing intricate models involving a combination of stochastic and deterministic operations, enabling, for example, attention, memory, and control actions.

• The paper introduces stochastic computation graphs to efficiently estimate gradients for models with both deterministic and stochastic components.
• It integrates pathwise derivative and score function estimators to enable backpropagation through complex probabilistic structures.
• The approach enhances computational efficiency and reduces variance in applications like reinforcement learning and variational inference.

Overview of "Gradient Estimation Using Stochastic Computation Graphs"

The paper "Gradient Estimation Using Stochastic Computation Graphs" by Schulman et al. introduces a formalism for efficiently estimating gradients in models where loss functions are represented by expectations over random variables. This is prevalent in machine learning problems spanning supervised, unsupervised, and notably, reinforcement learning. The primary contribution lies in the introduction and application of stochastic computation graphs (SCGs), which are directed acyclic graphs that incorporate both deterministic functions and probabilistic distributions.

Stochastic Computation Graphs (SCGs)

Stochastic computation graphs are defined with three node types: input nodes, deterministic nodes, and stochastic nodes. The structure uses edges to delineate dependencies among these nodes, enabling a systematic breakdown of the computation surrounding loss functions. The innovative aspect of the SCGs is their ability to encompass complex models that involve intricate blends of stochastic and deterministic elements—a common occurrence in modern deep learning architectures with mechanisms such as attention and memory.

Derivation of Gradient Estimators

At the heart of the paper is the derivation of unbiased gradient estimators for expected loss functions within SCGs. Schulman et al. establish that by augmenting the backpropagation algorithm, researchers can compute gradient estimators efficiently even when the loss functions include an expectation over random variables. The method couples the traditional pathwise derivative (PD) estimators and score function (SF) estimators, showcasing their applicability across different parameter configurations within the graph structure.

The paper highlights two crucial equivalent forms for the gradient estimator: an upstream gradient sum and its reformulation as a downstream cost sum. These formulations allow the computation to backpropagate through a SCG similarly to how derivatives are backpropagated in deterministic neural networks.

Surrogate Loss Functions and Practical Implications

Schulman et al. propose that practitioners can equate a surrogate objective to compute the required gradients using automatic differentiation tools. The surrogate function juxtaposes log probabilities of variables, leveraging the cost dependencies sampled during estimation. This method, significantly enhancing computational efficiency, extends the versatile utility of SCGs to broader machine learning applications, including probabilistic models with intractable summations.

The methodology also demonstrates robustness by detailing variance reduction techniques. Specifically, by integrating baselines dependent on non-influential nodes, the variance inherent in SF estimators can be significantly reduced, underpinning the reliability of the estimated gradients.

Applications in Machine Learning and Reinforcement Learning

The implications of this work are profound for fields that rely heavily on estimation involving stochastic processes. In variational inference, the framework supports complex latent variable models by facilitating stable and computationally feasible optimization of their parameters. For reinforcement learning, the SCG approach supports policy gradient methods by enabling gradient computation in environments where dynamics can only be simulated rather than explicitly modeled.

Conclusion and Future Directions

In conclusion, this work formalizes a versatile and efficient approach to gradient estimation, catering especially to models combining stochastic and deterministic processes. This framework paves the way for future research to explore more advanced architectures and algorithms within machine learning and AI. As models grow in complexity, the need for such efficient and scalable computation will only magnify, making stochastic computation graphs not only relevant but essential in the continuous advancement of AI technologies. Future developments might include integration with advanced automatic differentiation software or adaptations that cater to higher-order gradients, further enriching its application landscape.