Scaling Optimization Over Uncertainty via Compilation
Minsung Cho, John Gouwar, Steven Holtzen
TL;DR
This work introduces BBIR, a branch-and-bound intermediate representation, as a scalable target for optimization over discrete probabilistic inference. By combining lattice semirings with a compatible total order and leveraging algebraic model counting, BBIR enables efficient upper-bounding of partial policies and supports staged compilation for meta-optimization. The authors instantiate two languages, $\textsc{dappl}$ for MEU and $\textsc{pineappl}$ for MMAP, both compiling to BBIR and supported by a general branch-and-bound algorithm, with proofs of robustness and correctness. Empirical results show superior performance of the BBIR-based approach on MEU and MMAP tasks across Bayesian networks and gridworlds, while staged compilation significantly improves handling of nested MMAP queries. The framework broadens the applicability of knowledge compilation to optimization over inference and lays groundwork for richer decision-theoretic languages built on BBIR.
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.