Scaling Optimization Over Uncertainty via Compilation

TL;DR

This paper introduces a novel compilation-based optimization approach over probabilistic inference problems, using a new IR with binary decision diagrams and branch-and-bound, enabling scalable and staged optimization.

Contribution

The paper presents a new IR and optimization method that automatically factorizes and prunes probabilistic problems, supporting staged compilation and two language implementations for decision making and inference.

Findings

Effective optimization over probabilistic inference tasks.

Supports staged compilation for iterative querying.

Two languages, dappl and pineappl, demonstrate versatility.

Abstract

Probabilistic inference is fundamentally hard, yet many tasks require optimization on top of inference, which is even harder. We present a new optimization-via-compilation strategy to scalably solve a certain class of such problems. In particular, we introduce a new intermediate representation (IR), binary decision diagrams weighted by a novel notion of branch-and-bound semiring, that enables a scalable branch-and-bound based optimization procedure. This IR automatically factorizes problems through program structure and prunes suboptimal values via a straightforward branch-and-bound style algorithm to find optima. Additionally, the IR is naturally amenable to staged compilation, allowing the programmer to query for optima mid-compilation to inform further executions of the program. We showcase the effectiveness and flexibility of the IR by implementing two performant languages that both compile to it: dappl and pineappl. dappl is a functional language that solves maximum expected utility problems with first-class support for rewards, decision making, and conditioning. pineappl is an imperative language that performs exact probabilistic inference with support for nested marginal maximum a posteriori (MMAP) optimization via staging.