WHEN TO MAKE AND BREAK COMMITMENTS?

Abstract

In many scenarios, decision-makers must commit to long-term actions until their resolution before receiving the payoff of said actions, and usually, staying committed to such actions incurs continual costs. For instance, in healthcare, a newlydiscovered treatment cannot be marketed to patients until a clinical trial is conducted, which both requires time and is also costly. Of course in such scenarios, not all commitments eventually pay off. For instance, a clinical trial might end up failing to show efficacy. Given the time pressure created by the continual cost of keeping a commitment, we aim to answer: When should a decision-maker break a commitment that is likely to fail-either to make an alternative commitment or to make no further commitments at all? First, we formulate this question as a new type of optimal stopping/switching problem called the optimal commitment problem (OCP). Then, we theoretically analyze OCP, and based on the insight we gain, propose a practical algorithm for solving it. Finally, we empirically evaluate the performance of our algorithm in running clinical trials with subpopulation selection.

1. INTRODUCTION

In many real-world settings, decision-makers must commit to long-term actions and wait until their resolution before receiving the payoff of said actions. Meanwhile, staying committed to such actions incurs continual costs. For instance, in portfolio management, it might take time for an asset to develop additional value after an initial investment, and keeping capital tied up in an asset comes with an opportunity cost for the investor (Markowitz, 1959; Merton, 1969; Karatzas and Wang, 2020) . In an energy network, turning power stations on and off is not an immediate action, hence a sudden increase in energy demand can only be met with a delay after putting more stations into operation, and keeping stations operational obviously consumes resources (Rafique and Jianhua, 2018; Olofsson et al., 2022) . In healthcare, a newly-discovered treatment can only be marketed to patients once a successful clinical trial that targets the said treatment is conducted, which both requires time and is also costly (Kaitin, 2010; Umscheid et al., 2011) . Of course, not all commitments eventually pay off: An asset might end up losing value despite investments, energy demands might shift faster than a network can react to, and a clinical trial might fail to show efficacy for the targeted treatment. Given the time pressure created by the continual cost of keeping a commitment, our goal in this paper is to answer the question: When should a decision-maker break a commitment-thereby avoiding future costs but also forfeiting any potential returns-either to make an alternative commitment instead or to make no further commitments at all? Solving this problem optimally requires a careful balance between exploration and exploitation: The earlier a commitment that is bound to fail is broken, the more resources would be saved (cf. exploitation); but the longer one is kept, the more information is revealed regarding whether the commitment is actually failing or might still succeed (cf. exploration)-and in certain cases, also regarding the prospects of similar commitments one could make instead. Related problems are mostly studied within the context of adaptive experimentation and sequential hypothesis testing (see Section 5). As such, we focus on adaptive experimentation as our main application as well. More specifically, we consider the problem of selecting the target population of an adaptive experiment. Suppose an experimenter, who is interested in proving the efficacy of a new treatment, starts running an initial experiment that targets a certain population of patients. Incidentally, the treatment being tested is effective only for a relatively narrow subpopulation of patients but not for the wider population as a whole. Hence, an experiment targeting the overall population, but not the subpopulation specifically, will most probably fail to prove efficacy and prevent the deployment of the treatment for the patients who would have actually benefited from it, not to mention waste

