Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with unmeasured confounding, one should pursue individualized decision-making using partial identification in a comprehensive manner. We establish a formal link between individualized decision-making under partial identification and classical decision theory by considering a lower bound perspective of value/utility function. Secondly, building on this unified framework, we provide a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision-making/policy assignment. Lastly, we provide an interesting paradox drawing on novel connections between two challenging domains, that is, individualized decision-making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this article would in principle apply for a rich set of bounds that might be available under partial identification.

This paper extends my research applying statistical decision theory to treatment choice with sample data, using maximum regret to evaluate the performance of treatment rules. The specific new contribution is to study as-if optimization using estimates of illness probabilities in clinical choice between surveillance and aggressive treatment. Beyond its specifics, the paper sends a broad message. Statisticians and computer scientists have addressed conditional prediction for decision making in indirect ways, the former applying classical statistical theory and the latter measuring prediction accuracy in test samples. Neither approach is satisfactory. Statistical decision theory provides a coherent, generally applicable methodology.

The parameters for a Markov Decision Process (MDP) often cannot be specified exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets which the parameters belong to. Minimax regret has been proposed as an objective for planning in UMDPs to find robust policies which are not overly conservative. In this work, we focus on planning for Stochastic Shortest Path (SSP) UMDPs with uncertain cost and transition functions. We introduce a Bellman equation to compute the regret for a policy. We propose a dynamic programming algorithm that utilises the regret Bellman equation, and show that it optimises minimax regret exactly for UMDPs with independent uncertainties. For coupled uncertainties, we extend our approach to use options to enable a trade off between computation and solution quality. We evaluate our approach on both synthetic and real-world domains, showing that it significantly outperforms existing baselines.

In cooperative multiagent planning, it can often be beneficial for an agent to make commitments about aspects of its behavior to others, allowing them in turn to plan their own behaviors without taking the agent's detailed behavior into account. Extending previous work in the Bayesian setting, we consider instead a worst-case setting in which the agent has a set of possible environments (MDPs) it could be in, and develop a commitment semantics that allows for probabilistic guarantees on the agent's behavior in any of the environments it could end up facing. Crucially, an agent receives observations (of reward and state transitions) that allow it to potentially eliminate possible environments and thus obtain higher utility by adapting its policy to the history of observations. We develop algorithms and provide theory and some preliminary empirical results showing that they ensure an agent meets its commitments with history-dependent policies while minimizing maximum regret over the possible environments.

The increasing use of group discounts has provided opportunities for buying groups with diverse preferences to coordinate their behavior in order to exploit the best offers from multiple vendors. We analyze this problem from the viewpoint of the vendors, asking under what conditions a vendor should adopt a volume-based price schedule rather than posting a fixed price, either as a monopolist or when competing with other vendors. When vendors have uncertainty about buyers' valuations specified by a known distribution, we show that a vendor is always better off posting a fixed price, provided that buyers' types are i.i.d. and that other vendors also use fixed prices. We also show that these assumptions cannot be relaxed: if buyers are not i.i.d., or other vendors post discount schedules, then posting a schedule may yield higher profit for the vendor. We provide similar results under a distribution-free uncertainty model, where vendors minimize their maximum regret over all type realizations.