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Non-exponential Reward Discounting in Reinforcement Learning

Proceedings of the AAAI Conference on Artificial Intelligence, 2023
Reinforcement learning methods typically discount future rewards using an exponential scheme to achieve theoretical convergence guarantees. Studies from neuroscience, psychology, and economics suggest that human and animal behavior is better captured by the hyperbolic discounting model.
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Discounted MDP’s: Distribution Functions and Exponential Utility Maximization

SIAM Journal on Control and Optimization, 1987
The present value of the rewards associated with a discrete-time Markov process has a probability distribution which depends on the initial state. The first part of the paper applies fixed point theory to a system of equations for the distribution functions of the present value.
Chung, Kun-Jen, Sobel, Matthew J.
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The Pareto Comparisons of a Group of Exponential Discounters

Mathematics of Operations Research, 2020
Agents with different discount factors disagree about some intertemporal trade-offs, but they will also agree sometimes. We seek to understand precisely the nature of their agreements and disagreements. A group of agents is identified with a set of discount factors.
Christopher P. Chambers   +1 more
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Functional limit theorems for discounted exponential functional of random walk and discounted convergent perpetuity

Statistics & Probability Letters, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexander Iksanov, Oleh Kondratenko
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RENEWAL THEORY WITH EXPONENTIAL AND HYPERBOLIC DISCOUNTING

Probability in the Engineering and Informational Sciences, 2007
To determine optimal investment and maintenance decisions, the total costs should be minimized over the whole life of a system or structure. In minimizing life-cycle costs, it is important to account for the time value of money by discounting and to consider the uncertainties involved. This article presents new results in renewal theory with costs that
J. A. M. van der Weide   +2 more
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Patient Decision Making: Exponential versus Hyperbolic Discounting

Managerial and Decision Economics, 2012
Evidence strongly indicates that human decision makers discount the future using a hyperbolic function instead of following an exponential, which has been the long‐standing assumption. We compare the exponential and hyperbolic models in evaluation of a simple research and development project selection problem, finding that the exponential function ...
Samuel B. Graves, Jeffrey L. Ringuest
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Aggregate savings under quasi-hyperbolic versus exponential discounting

Economics Letters, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Exponential linear quadratic optimal control with discounting

IEEE Transactions on Automatic Control, 1994
The author considers optimal problems when the state \(x(t)\) is solution of an \(n\)-dimensional linear stochastic differential equation \(dx= (Ax+ Bu)dt+ Gdw\), \(0\leq t\leq T\), where \(w\) is a Wiener process. The first problem is associated with the discounted functional: \[ I={1\over 2} \int^{T-\lambda t}_ 0 e(x^ t Qx+ u^ t Ru)+ {1\over 2} e^{- \
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Non-Exponential Discounting: A Direct Test [PDF]

open access: possible, 2008
Standard models of intertemporal utility maximization under uncertainty assume that agents discount future utility flows at a constant compounded rate—exponential discounting. Euler equations estimated over different time horizons should have equal discount rates. They do not.
Richard Startz, Kwok Ping Tsang
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Consumption–investment strategies with non-exponential discounting and logarithmic utility

European Journal of Operational Research, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, Qian, Shen, Yang, Wei, Jiaqin
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