Functional Sequential Treatment Allocation

Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present paper we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies

From Wald to Savage: homo economicus becomes a Bayesian statistician

Bayesian rationality is the paradigm of rational behavior in neoclassical economics. A rational agent in an economic model is one who maximizes her subjective expected utility and consistently revises her beliefs according to Bayes’s rule. The paper raises the question of how, when and why this characterization of rationality came to be endorsed by mainstream economists. Though no definitive answer is provided, it is argued that the question is far from trivial and of great historiographic importance. The story begins with Abraham Wald’s behaviorist approach to statistics and culminates with Leonard J. Savage’s elaboration of subjective expected utility theory in his 1954 classic The Foundations of Statistics. It is the latter’s acknowledged fiasco to achieve its planned goal, the reinterpretation of traditional inferential techniques along subjectivist and behaviorist lines, which raises the puzzle of how a failed project in statistics could turn into such a tremendous hit in economics. A couple of tentative answers are also offered, involving the role of the consistency requirement in neoclassical analysis and the impact of the postwar transformation of US business schools.Savage, Wald, rational behavior, Bayesian decision theory, subjective probability, minimax rule, statistical decision functions, neoclassical economics

When starting with the most expensive option makes sense : use and misuse of marginal abatement cost curves

This article investigates the use of expert-based Marginal Abatement Cost Curves (MACC) to design abatement strategies. It shows that introducing inertia, in the form of the"cost in time"of available options, changes significantly the message from MACCs. With an abatement objective in cumulative emissions (e.g., emitting less than 200 GtCO2 in the 2000-2050 period), it makes sense to implement some of the more expensive options before the potential of the cheapest ones has been exhausted. With abatement targets expressed in terms of emissions at one point in time (e.g., reducing emissions by 20 percent in 2020), it can even be preferable to start with the implementation of the most expensive options if their potential is high and their inertia significant. Also, the best strategy to reach a short-term target is different depending on whether this target is the ultimate objective or there is a longer-term target. The best way to achieve Europe's goal of 20 percent reduction in emissions by 2020 is different if this objective is the ultimate objective or if it is only a milestone in a trajectory toward a 75 percent reduction in 2050. The cheapest options may be sufficient to reach the 2020 target but could create a carbon-intensive lock-in and preclude deeper emission reductions by 2050. These results show that in a world without perfect foresight and perfect credibility of the long-term carbon-price signal, a unique carbon price in all sectors is not the most efficient approach. Sectoral objectives, such as Europe's 20 percent renewable energy target in Europe, fuel-economy standards in the auto industry, or changes in urban planning, building norms and infrastructure design are a critical part of an efficient mitigation policy.Climate Change Mitigation and Green House Gases,Climate Change Economics,Environment and Energy Efficiency,Energy and Environment,Transport and Environment

Making and Keeping Probabilistic Commitments for Trustworthy Multiagent Coordination

In a large number of real world domains, such as the control of autonomous vehicles, team sports, medical diagnosis and treatment, and many others, multiple autonomous agents need to take actions based on local observations, and are interdependent in the sense that they rely on each other to accomplish tasks. Thus, achieving desired outcomes in these domains requires interagent coordination. The form of coordination this thesis focuses on is commitments, where an agent, referred to as the commitment provider, specifies guarantees about its behavior to another, referred to as the commitment recipient, so that the recipient can plan and execute accordingly without taking into account the details of the provider's behavior. This thesis grounds the concept of commitments into decision-theoretic settings where the provider's guarantees might have to be probabilistic when its actions have stochastic outcomes and it expects to reduce its uncertainty about the environment during execution. More concretely, this thesis presents a set of contributions that address three core issues for commitment-based coordination: probabilistic commitment adherence, interpretation, and formulation. The first contribution is a principled semantics for the provider to exercise maximal autonomy that responds to evolving knowledge about the environment without violating its probabilistic commitment, along with a family of algorithms for the provider to construct policies that provably respect the semantics and make explicit tradeoffs between computation cost and plan quality. The second contribution consists of theoretical analyses and empirical studies that improve our understanding of the recipient's interpretation of the partial information specified in a probabilistic commitment; the thesis shows that it is inherently easier for the recipient to robustly model a probabilistic commitment where the provider promises to enable preconditions that the recipient requires than where the provider instead promises to avoid changing already-enabled preconditions. The third contribution focuses on the problem of formulating probabilistic commitments for the fully cooperative provider and recipient; the thesis proves structural properties of the agents' values as functions of the parameters of the commitment specification that can be exploited to achieve orders of magnitude less computation for 1) formulating optimal commitments in a centralized manner, and 2) formulating (approximately) optimal queries that induce (approximately) optimal commitments for the decentralized setting in which information relevant to optimization is distributed among the agents.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162948/1/qizhg_1.pd

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment