Learning and Model Validation

This paper studies the following problem. An agent takes actions based on a possibly misspecified model. The agent is 'large', in the sense that his actions influence the model he is trying to learn about. The agent is aware of potential model misspecification and tries to detect it, in real-time, using an econometric specification test. If his model fails the test, he formulates a new better-fitting model. If his model passes the test, he uses it to formulate and implement a policy based on the provisional assumption that the current model is correctly specified, and will not change in the future. We claim that this testing and model validation process is an accurate description of most macroeconomic policy problems. Unfortunately, the dynamics produced by this process are not well understood. We make progress on this problem by relating it to a problem that is well understood. In particular, we relate it to the dynamics of constant-gain stochastic approximation algorithms. This enables us to appeal to well known results from the large deviations literature to help us understand the dynamics of testing and model revision. We show that as the agent applies an increasingly stringent specification test, the large deviation properties of the discrete model validation dynamics converge to those of the continuous learning dynamics. This sheds new light on the recent constant-gain learning literature.Learning, Validation, Relative Entropy, Large Deviation

Robustness

The standard theory of decision making under uncertainty advises the decision maker to form a statistical model linking outcomes to decisions and then to choose the optimal distribution of outcomes. This assumes that the decision maker trusts the model completely. But what should a decision maker do if the model cannot be trusted? Lars Hansen and Thomas Sargent, two leading macroeconomists, push the field forward as they set about answering this question. They adapt robust control techniques and apply them to economics. By using this theory to let decision makers acknowledge misspecification in economic modeling, the authors develop applications to a variety of problems in dynamic macroeconomics. Technical, rigorous, and self-contained, this book will be useful for macroeconomists who seek to improve the robustness of decision-making processes.decision-making, uncertainty, statistical models, control techniques, economic modeling, dynamic microeconomics, misspecification

Approximating Value Equivalence in Interactive Dynamic Influence Diagrams Using Behavioral Coverage

Interactive dynamic influence diagrams (I-DIDs) provide an explicit way of modeling how a subject agent solves decision making problems in the presence of other agents in a common setting. To optimize its decisions, the subject agent needs to predict the other agents' behavior, that is generally obtained by solving their candidate models. This becomes extremely difficult since the model space may be rather large, and grows when the other agents act and observe over the time. A recent proposal for solving I-DIDs lies in a concept of value equivalence (VE) that shows potential advances on significantly reducing the model space. In this paper, we establish a principled framework to implement the VE techniques and propose an approximate method to compute VE of candidate models. The development offers ample opportunity of exploiting VE to further improve the scalability of I-DID solutions. We theoretically analyze properties of the approximate techniques and show empirical results in multiple problem domains

An Interview with Thomas J. Sargent

The rational expectations hypothesis swept through macroeconomics during the 1970’s and permanently altered the landscape. It remains the prevailing paradigm in macroeconomics, and rational expectations is routinely used as the standard solution concept in both theoretical and applied macroeconomic modelling. The rational expectations hypothesis was initially formulated by John F. Muth Jr. in the early 1960s. Together with Robert Lucas Jr., Thomas (Tom) Sargent pioneered the rational expectations revolution in macroeconomics in the 1970s. We interviewed Tom Sargent for Macroeconomic Dynamics .

A value equivalence approach for solving interactive dynamic influence diagrams

Interactive dynamic influence diagrams (I-DIDs) are recognized graphical models for sequential multiagent decision making under uncertainty. They represent the problem of how a subject agent acts in a common setting shared with other agents who may act in sophisticated ways. The difficulty in solving I-DIDs is mainly due to an exponentially growing space of candidate models ascribed to other agents over time. in order to minimize the model space, the previous I-DID techniques prune behaviorally equivalent models. In this paper, we challenge the minimal set of models and propose a value equivalence approach to further compress the model space. The new method reduces the space by additionally pruning behaviourally distinct models that result in the same expected value of the subject agent’s optimal policy. To achieve this, we propose to learn the value from available data particularly in practical applications of real-time strategy games. We demonstrate the performance of the new technique in two problem domains

Student Uncertainty and Major Choice

This paper examines how model uncertainty affects students\u27 choice of major. To account for this uncertainty, the students apply a max-min operator to their optimization problem. We show analytically that greater uncertainty in a particular major causes the student to be less likely to choose that major and that greater uncertainty across all majors causes fewer students to major in science, technology, engineering, and math. To test the model\u27s assumptions and predictions, we have conducted a novel survey of college freshmen. The results from this survey are consistent with assumptions and implications of the theoretical model

A value equivalence approach for solving interactive dynamic influence diagrams

Interactive dynamic influence diagrams (I-DIDs) are recognized graphical models for sequential multiagent decision making under uncertainty. They represent the problem of how a subject agent acts in a common setting shared with other agents who may act in sophisticated ways. The difficulty in solving I-DIDs is mainly due to an exponentially growing space of candidate models ascribed to other agents over time. in order to minimize the model space, the previous I-DID techniques prune behaviorally equivalent models. In this paper, we challenge the minimal set of models and propose a value equivalence approach to further compress the model space. The new method reduces the space by additionally pruning behaviourally distinct models that result in the same expected value of the subject agent’s optimal policy. To achieve this, we propose to learn the value from available data particularly in practical applications of real-time strategy games. We demonstrate the performance of the new technique in two problem domains

A neurally plausible model learns successor representations in partially observable environments

Animals need to devise strategies to maximize returns while interacting with their environment based on incoming noisy sensory observations. Task-relevant states, such as the agent's location within an environment or the presence of a predator, are often not directly observable but must be inferred using available sensory information. Successor representations (SR) have been proposed as a middle-ground between model-based and model-free reinforcement learning strategies, allowing for fast value computation and rapid adaptation to changes in the reward function or goal locations. Indeed, recent studies suggest that features of neural responses are consistent with the SR framework. However, it is not clear how such representations might be learned and computed in partially observed, noisy environments. Here, we introduce a neurally plausible model using distributional successor features, which builds on the distributed distributional code for the representation and computation of uncertainty, and which allows for efficient value function computation in partially observed environments via the successor representation. We show that distributional successor features can support reinforcement learning in noisy environments in which direct learning of successful policies is infeasible