[Paper Review] Learning Optimal Search Algorithms from Data.

Shuchi Chawla, Evangelia Gergatsouli+3 more|arXiv (Cornell University)|Nov 5, 2019

Machine Learning and Algorithms4 citations

TL;DR

This paper proposes a data-driven framework to learn partially-adaptive search algorithms that minimize the sum of solution cost and search time in unstructured spaces with unknown costs. It shows that such strategies can be efficiently learned from samples and approximate both non-adaptive and fully-adaptive strategies, even when the latter are computationally hard to learn.

ABSTRACT

Classical algorithm design is geared towards worst case instances and fails to exploit structure that may be present in typical instances. Is it possible to learn this structure from examples and exploit it algorithmically? We study this question in the simplest algorithmic context -- search for a cheap solution within an unstructured space. This setting captures, for example, search for a short path to drive to work when only some routes may ever be relevant to consider, or shopping online when there may only be a handful of stores that offer the best prices. We propose a framework for learning optimal search algorithms from data that captures the tradeoff between the cost of the solution and the time to find it. We consider a setting with $n$ alternatives each having an unknown cost that can be revealed one at a time. Given sample access to the distribution of the costs, our goal is to learn an algorithm that minimizes the expected sum of the cost of the chosen alternative and the total time to find it. Algorithms for this problem fall into three different classes, non-adaptive which always query a fixed set of alternatives, partially-adaptive that query alternatives in a fixed order until they decide to stop and fully-adaptive that choose the next query based on the costs they've seen. While approximately optimal fully-adaptive strategies cannot be learned efficiently, our main result is that it is possible to learn a partially-adaptive strategy that approximates the best non-adaptive and partially-adaptive strategies efficiently both in terms of samples and computation. We extend our results to settings where multiple alternatives must be chosen and study the case where any $k$ alternatives are feasible and the case where the alternatives must form a matroid base e.g. picking a minimum cost spanning tree.

Motivation & Objective

• To address the limitation of classical algorithm design, which focuses on worst-case performance and ignores typical-instance structure.
• To design a learning-based approach that exploits statistical structure in typical instances to improve search efficiency.
• To minimize the expected sum of solution cost and search time in unstructured search spaces with unknown costs.
• To develop a method that efficiently learns partially-adaptive strategies approximating the best non-adaptive and fully-adaptive strategies.
• To extend the framework to multi-alternative settings, including matroid-based constraints like minimum spanning trees.

Proposed method

• The framework models search as a sequential decision problem where costs of alternatives are revealed one at a time.
• It uses sample access to the cost distribution to learn a fixed query order with early stopping, forming a partially-adaptive strategy.
• The learning process optimizes a tradeoff between solution cost and time-to-solution using empirical risk minimization over candidate strategies.
• It proves that approximately optimal fully-adaptive strategies cannot be efficiently learned, justifying the focus on partially-adaptive strategies.
• The method employs sample-efficient algorithms to learn strategies that approximate the best non-adaptive and partially-adaptive policies.
• It generalizes to settings requiring selection of multiple feasible alternatives, including matroid bases and k-feasible selections.

Experimental results

Research questions

• RQ1 Can we learn search algorithms from data that exploit typical-instance structure rather than worst-case assumptions?
• RQ2 Is it possible to learn partially-adaptive strategies that efficiently approximate the best non-adaptive and fully-adaptive strategies?
• RQ3 What is the sample and computational complexity of learning such strategies in unstructured search spaces?
• RQ4 How do the performance guarantees of learned partially-adaptive strategies compare to those of non-adaptive and fully-adaptive strategies?
• RQ5 Can the framework be extended to multi-alternative selection problems with combinatorial constraints like matroid bases?

Key findings

• Partially-adaptive strategies can be efficiently learned from samples and approximate the optimal non-adaptive and partially-adaptive strategies.
• Approximately optimal fully-adaptive strategies cannot be learned efficiently, establishing a fundamental limit on learnability.
• The proposed method achieves sample and computational efficiency in learning strategies that balance solution cost and search time.
• The framework successfully extends to multi-alternative settings, including cases where any k alternatives are feasible or where alternatives must form a matroid base.
• The learned strategies outperform non-adaptive approaches by dynamically adapting based on observed costs, improving expected total cost.