Utilitarian Algorithm Configuration for Infinite Parameter Spaces

TL;DR

This work addresses the limitation of prior utilitarian algorithm configuration methods that are restricted to finite parameter spaces by introducing COUP, a continuous, optimistic, UCB-based procedure for searching infinite configuration spaces. COUP extends the finite-space OUP by operating in phases over expanding candidate sets and guaranteeing $(\epsilon,\gamma)$-optimality with high probability, while maintaining strong theoretical bounds and practical efficiency. Empirically, COUP and its finite counterpart OUP outperform or match existing baselines across datasets and utilities, and COUP's phase-based exploration proves effective with only modest overhead when scaling to large configuration spaces. The approach substantially broadens the applicability of utilitarian configuration to continuous domains, enabling faster, principled parameter optimization in real-world settings.

Abstract

Utilitarian algorithm configuration is a general-purpose technique for automatically searching the parameter space of a given algorithm to optimize its performance, as measured by a given utility function, on a given set of inputs. Recently introduced utilitarian configuration procedures offer optimality guarantees about the returned parameterization while provably adapting to the hardness of the underlying problem. However, the applicability of these approaches is severely limited by the fact that they only search a finite, relatively small set of parameters. They cannot effectively search the configuration space of algorithms with continuous or uncountable parameters. In this paper we introduce a new procedure, which we dub COUP (Continuous, Optimistic Utilitarian Procrastination). COUP is designed to search infinite parameter spaces efficiently to find good configurations quickly. Furthermore, COUP maintains the theoretical benefits of previous utilitarian configuration procedures when applied to finite parameter spaces but is significantly faster, both provably and experimentally.

Figures (7)

• Figure 1: The $\epsilon$ guaranteed by each procedure as a function of total runtime using the log-Laplace utility function (top row) and uniform utility function (bottom row). OUP consistently outperforms both UP and the naive procedure for reasonable values of $\epsilon$, often by an order of magnitude and even when the the parameter of the naive procedure has been well-chosen.
• Figure 2: Total time spent by OUP on each configuration (log-Laplace utility function). Configurations are sorted according to average utility. OUP spends less time on all but the very best configurations.
• Figure 3: Performance of COUP compared to OUP, using the log-Laplace utility function. COUP is anytime, but takes only a small factor more time than OUP. The bottom row shows the final times. OUP backtracks on the cplex_region dataset because COUP sampled a relatively good configuration in phase 5, which OUP is able to capitalize on, proving optimality in less total time than in phase 4.
• Figure 4: Different schedules for exploring new configurations (refining $\gamma$) vs. exploring existing configurations (refining $\epsilon$) when running COUP. Results are for the log-Laplace utility function and the cplex_rcw dataset.
• Figure 5: Average configurator performance as measured by the percentage gap to best configuration in the dataset. Top row shows procedures optimizing the log-Laplace utility function. Bottom row shows procedures optimizing an expected runtime. Error regions show maximum and minimum observations.

Theorems & Definitions (15)

• Definition 1: $\epsilon$-optimal
• Lemma 1
• Lemma 2
• Theorem 1
• Definition 2: $(\epsilon, \gamma)$-optimal
• Lemma 3
• Lemma 4
• Lemma 5
• Theorem 2
• proof