Adaptive strategies in Kelly’s horse races model

Armand, Despons,; Peliti, Luca; Lacoste, David

doi:10.1088/1742-5468/ac8e58

Cited by 8 publications

(4 citation statements)

References 22 publications

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“…These fitness trajectories are reminiscent of the dynamics of learning through adaptive strategies in gambling problems, where an initial phase of loss of capital due to the cost of learning is followed by recovery [57]. Although, at the level of a single organism, the fitness effects of new mutations are independent of the history of mutations that came before, natural selection endows populations with a form of memory [58, 59].…”

Section: Resultsmentioning

confidence: 99%

Gene Birth in a Model of Non-genic Adaptation

Mani

Tlusty²

2022

Preprint

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Over evolutionary timescales, genomic loci switch between functional and non-functional states through processes such as pseudogenization and de novo gene birth. Here we ask about the likelihood and rate of functionalization of non-functional loci. We simulate an evolutionary model to look at the contributions of mutations and structural variation using biologically reasonable distributions of mutational effects. We find that a wide range of mutational effects are conducive to functionalization, thus indicating the ubiquity of this process. During functionalization, loci transition from a mutation dominated 'learning' phase to a selection dominated adaptation phase. Interestingly, in the special case of de novo gene birth, whereby non-functional loci begin to express a functional product, we find that expression level changes lead to rare, extreme jumps in fitness, whereas sustained adaptation is driven by product functionality. Our work supports the idea that the potential for adaptation is spread widely across the genome, and our results offer mechanistic insights into the process of de novo gene birth.

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Section: Resultsmentioning

confidence: 99%

Gene Birth in a Model of Non-genic Adaptation

Mani

Tlusty²

2022

Preprint

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“…In subsequent work, we found a similar trade-off in the context of a biological population with phenotypic switching in a fluctuating environment [17] by building on a piece-wise Markov model introduced earlier [18]. We have also proposed an adaptive version of Kelly’s gambling based on Bayesian inference [19].…”

Section: Introductionmentioning

confidence: 84%

The trade-off between growth and risk in Kelly’s gambling and beyond

Cavallero,

Rousselot,

Pugatch

et al. 2023

Preprint

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We study a generalization of Kelly’s horse model to situations where gambling on horses other than the winning horse does not lead to a complete loss of the investment. In such a case, the odds matrix is non-diagonal, a case which is of special interest for biological applications. We derive a trade-off for this model between the mean growth rate and the volatility as a proxy for risk. We show that this trade-off is related to a game-theoretic formulation of this problem developed previously. Since the effect of fluctuations around the average growth rate is asymmetric, we also study how the risk-growth trade-off is modified when risk is evaluated more accurately by the probability of the gamble’s ruin.

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“…Finally, we mention one additional continuation of this research which is motivated by the following observation: An adaptive controller aimed at maximizing expected logarithmic growth, say along the lines of those given in recent papers such as [19] and [20], should rightfully be viewed as a member of our admissible control set K. Accordingly, our plan for future research involves exploring the connection between results in adaptive and nonlinear control which have traditionally been viewed as rather separate areas. In this regard, further motivation for such work is provided by the simple example provided for n = 2.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

“…In this regard, further motivation for such work is provided by the simple example provided for n = 2. For this low-dimensional example, our optimal three-gain robust nonlinear controller turns out to be the same as the one provided in [19].…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case

Proskurnikov¹,

Barmish²

2023

Preprint

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The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear feedback, the use of nonlinear control is conspicuously absent. This is epitomized by the large subset of this literature dealing with Kelly Betting. With this as the high-level motivation, we study the potential for use of nonlinear control in this framework. To this end, we consider a "demonstration case" which is one of the simplest scenarios encountered in this line of research: repeated flips of a biased coin with probability of heads p and even-money payoff on each flip. First, we formulate a new robust nonlinear control problem which we believe is both simple to understand and apropos for dealing with concerns about distributional robustness; i.e., instead of assuming that p is perfectly known as in the case of the classical Kelly formulation, we begin with a bounding set P ⊆ [0, 1] for this probability. Then, we provide a theorem, our main result, which gives a closed-form description of the optimal robust nonlinear controller and a corollary which establishes that it robustly outperforms linear controllers such as those found in the literature. A second contribution of this paper bears upon the computability of our solution. For an n-flip game, whereas an admissible controller has 2 n − 1 parameters, at the optimum only O(n 2 ) of them turn out to be distinct. Finally, we provide some illustrations comparing robust performance with what is possible when working with the so-called perfect-information Kelly optimum.

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Adaptive strategies in Kelly’s horse races model

Cited by 8 publications

References 22 publications

Gene Birth in a Model of Non-genic Adaptation

Gene Birth in a Model of Non-genic Adaptation

The trade-off between growth and risk in Kelly’s gambling and beyond

On the Benefit of Nonlinear Control for Robust Logarithmic Growth: Coin Flipping Games as a Demonstration Case

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