2012
DOI: 10.1063/1.3703647
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Process-conditioned investing with incomplete information using maximum causal entropy

Abstract: Abstract. Investing to optimally maximize the growth rate of wealth based on sequences of event outcomes has many information-theoretic interpretations. Namely, the mutual information characterizes the benefit of additional side information being available when making investment decisions [1] in settings where the probabilistic relationships between side information and event outcomes are known. Additionally, the relative variant of the principle of maximum entropy [2] provides the optimal investment allocatio… Show more

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Cited by 7 publications
(11 citation statements)
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“…Ziebart (2010) showed that minimizing the worst-case predictive loss results in a model where the probability of a sequence decreases exponentially with cost, p ( ξ | g ) exp ( C g normalu ( ξ ) ) . Importantly, one can efficiently learn a cost function consistent with this model from demonstrations (Ziebart et al, 2008).…”
Section: Frameworkmentioning
confidence: 99%
“…Ziebart (2010) showed that minimizing the worst-case predictive loss results in a model where the probability of a sequence decreases exponentially with cost, p ( ξ | g ) exp ( C g normalu ( ξ ) ) . Importantly, one can efficiently learn a cost function consistent with this model from demonstrations (Ziebart et al, 2008).…”
Section: Frameworkmentioning
confidence: 99%
“…For our one-step example, this results in the Bayes’ posterior It is straightforward to identify p des ( X ′) of Active Inference as a particular choice of a success probability p 0 ( R = 1| X ′), or equivalently, log p des ( X ′) as a reward function r = r ( X ′), so that the joint distribution (27) reduces to the reference function ϕ in (25) . Thus, the version of Active Inference in [ 101 ] is simply a variational formulation of Control as Inference that approximates exact posteriors of the form (28) , like other previous variational Bayes’ approaches [ 107 , 109 , 110 ].…”
Section: Variational Free Energy In Active Inferencementioning
confidence: 99%
“…Either an action distribution is built into the reference function, which presupposes optimal behavior by designing a value function Q that leads to desired consequences, or the outcome probability under the generative model p 0 is modified directly by multiplying p des to p 0 . The latter case is the variational version of Control as Inference, well-known in the machine learning literature [ 77 , 105 – 110 ]. Considering the issues of Q -value Active Inference discussed above, and the fact that Control as Inference does not rely on a desired distribution over outcomes, we could ask whether formulating preferences by assuming a desired distribution is well-advised.…”
Section: Variational Free Energy In Active Inferencementioning
confidence: 99%
“…In previous applications of the principle of maximum causal entropy [25], [26], [24], [29], the causal structure of the interacting processes was assumed. We investigate estimating this causal structure rather than assuming it in this work.…”
Section: Maximum Causal Entropymentioning
confidence: 99%
“…This corresponds to the L 0 norm of parameters associated with those constraints, shown in (24) With an appropriately chosen penalty weight, λ, the minimal structure that provides a feasible causally conditioned probability estimate would be optimal. Unfortunately, with α = 0, (24) can no longer be solved as a convex optimization problem. Both greedy approximations to the L 0 solution and relaxations to L 1 or L 2 penalties are instead possible.…”
Section: Structure Learning Formulationmentioning
confidence: 99%