Resource bounded randomness and its applications

Stull, Donald M.

doi:10.1017/9781108781718.010

Cited by 2 publications

(6 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The techniques are major adaptations of ideas from Huang and Stull [9], Rute [14], Ko [10] and Hoyrup and Rojas [4] together with new quantitative bounds on the convergence of ergodic averages. We also show that the space of EXPSPACE randoms defined in terms of EXPSPACE tests is a strict subset of PSPACE randoms as studied in Huang and Stull [16]. Our main contribution is the identification of the exact setting and notions of convergence which are amenable to proving convergence of ergodic averages on resource-bounded randoms, and these may be useful in investigating further dynamical systems in resource-bounded settings.…”

Section: Introductionmentioning

confidence: 91%

“…Henceforth, we study the notion of randomness on (Σ ∞ , µ). The following is the definition of PSPACE randomness from [16]. We also define its EXPSPACE analogue.…”

Section: The Function G : σmentioning

confidence: 99%

“…In this section, we briefly recall standard definitions for PSPACE computability of real numbers, sequences of real numbers, L 1 computable functions, and measure-preserving transformations. The justifications and proofs of equivalences of various notions are present in Stull's thesis [16]. Definition 3.1 (PSPACE computable number [16]).…”

Section: Pspace L 1 Computabilitymentioning

confidence: 99%

“…The justifications and proofs of equivalences of various notions are present in Stull's thesis [16]. Definition 3.1 (PSPACE computable number [16]). A real number a is PSPACE computable if there exists a PSPACE machine M such that for each…”

Section: Pspace L 1 Computabilitymentioning

confidence: 99%

“…Let us initially define PSPACE sequence of simple functions. Definition 3.2 (PSPACE sequence of simple functions [16]). A sequence of simple functions…”

Section: Pspace L 1 Computabilitymentioning

confidence: 99%

See 4 more Smart Citations

Ergodic Theorems for PSPACE functions and their converses

Nandakumar,

Pulari

2020

Preprint

View full text Add to dashboard Cite

We initiate the study of effective pointwise ergodic theorems in resource-bounded settings. Classically, the convergence to the ergodic averages for integrable functions can in general, be arbitrarily slow [11]. However, we show that for PSPACE L 1 functions and a class of PSPACE computable measure-preserving ergodic transformations, the ergodic average exists and is equal to the space average on every EXPSPACE random. Further, we show that the class of EXPSPACE randoms is a strict subset of the class of PSPACE randoms studied by Huang and Stull [9].

show abstract

Section: Introductionmentioning

confidence: 91%

“…Henceforth, we study the notion of randomness on (Σ ∞ , µ). The following is the definition of PSPACE randomness from [16]. We also define its EXPSPACE analogue.…”

Section: The Function G : σmentioning

confidence: 99%

Section: Pspace L 1 Computabilitymentioning

confidence: 99%

Section: Pspace L 1 Computabilitymentioning

confidence: 99%

“…Let us initially define PSPACE sequence of simple functions. Definition 3.2 (PSPACE sequence of simple functions [16]). A sequence of simple functions…”

Section: Pspace L 1 Computabilitymentioning

confidence: 99%

See 3 more Smart Citations

Ergodic Theorems for PSPACE functions and their converses

Nandakumar,

Pulari

2020

Preprint

View full text Add to dashboard Cite

show abstract

A Theory of Bounded Inductive Rationality

Oesterheld

Demski

Conitzer

2023

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical claims. This assumption is unrealistic when, for example, we offer bets on remote digits of π or when an agent faces a computationally intractable planning problem. Furthermore, the assumption of logical omniscience creates contradictions in cases where the environment can contain descriptions of the agent itself. Importantly, strategic interactions as studied in game theory are decision problems in which a rational agent is predicted by its environment (the other players). In this paper, we develop a theory of rational decision making that does not assume logical omniscience. We consider agents who repeatedly face decision problems (including ones like betting on digits of π or games against other agents). The main contribution of this paper is to provide a sensible theory of rationality for such agents. Roughly, we require that a boundedly rational inductive agent tests each efficiently computable hypothesis infinitely often and follows those hypotheses that keep their promises of high rewards. We then prove that agents that are rational in this sense have other desirable properties. For example, they learn to value random and pseudo-random lotteries at their expected reward. Finally, we consider strategic interactions between different agents and prove a folk theorem for what strategies bounded rational inductive agents can converge to.

show abstract

Resource bounded randomness and its applications

Cited by 2 publications

References 39 publications

Ergodic Theorems for PSPACE functions and their converses

Ergodic Theorems for PSPACE functions and their converses

A Theory of Bounded Inductive Rationality

Contact Info

Product

Resources

About