Reactive probabilistic programming

Abstract

Synchronous modeling is at the heart of programming languages like Lustre, Esterel, or SCADE used routinely for implementing safety critical control software, e.g., fly-bywire and engine control in planes. However, to date these languages have had limited modern support for modeling uncertainty -probabilistic aspects of the software's environment or behavior -even though modeling uncertainty is a primary activity when designing a control system.In this paper we present ProbZelus the first synchronous probabilistic programming language. ProbZelus conservatively provides the facilities of a synchronous language to write control software, with probabilistic constructs to model uncertainties and perform inference-in-the-loop.We present the design and implementation of the language. We propose a measure-theoretic semantics of probabilistic stream functions and a simple type discipline to separate deterministic and probabilistic expressions. We demonstrate a semantics-preserving compilation into a first-order functional language that lends itself to a simple presentation of inference algorithms for streaming models. We also redesign the delayed sampling inference algorithm to provide efficient streaming inference. Together with an evaluation on several reactive applications, our results demonstrate that ProbZelus enables the design of reactive probabilistic applications and efficient, bounded memory inference. CCS Concepts: • Theory of computation → Streaming models; • Software and its engineering → Data flow languages.

Programming and reasoning with partial observability

“…BLIMP's observe has a similar semantics to observe constructs in PPLs. BLIMP's infer, which enables the program itself to perform inference, has some support in PPLs as well [Baudart et al 2020;Staton 2017].…”

Statically bounded-memory delayed sampling for probabilistic streams

“…These languages provide programming constructs and tools for probabilistic modeling and automated inference. Researchers have developed probabilistic programming languages for several domains, including data science [Gelman et al 2015], machine learning [Bingham et al 2019;Tran et al 2017], scientific simulation [Baydin et al 2019], and real-time control [Baudart et al 2020].…”

“…For example, control for an airplane fly-by-wire system can be implemented as a program transforming a stream of altitude measurements into a stream of commands to the engine. Baudart et al [2020] introduced a probabilistic programming language, ProbZelus, to enable probabilistic programming in this domain of computations on streams. A key innovation of ProbZelus was to demonstrate that delayed sampling ] could be extended to work with streams to provide high-quality inference procedures.…”

“…The challenge in adapting delayed sampling to computations on streams is that such computations run for indefinite periods of time and are often subject to stringent limits on resources, such as memory. Baudart et al [2020] showed that, in many cases, only a finite number of nodes in delayed sampling's graph data structures were reachable at any given time, and the rest could not influence the computation in the future and could be removed from memory. However, this behavior depends on the probabilistic model under consideration; delayed sampling is not guaranteed to maintain a bounded amount of memory for all programs.…”

“…In Section 2, we give an example program to illustrate the concepts in the paper. In Section 3, we present the syntax and semantics of a language for probabilistic programming with streams, adapted from the 𝜇𝐹 language from Baudart et al [2020]. In Section 4, we review background on delayed sampling, based on the contributions from and Baudart et al [2020].…”