3 problems

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Whittle's asymptotic optimality conjecture for restless multi-armed bandits
A restless multi-armed bandit problem has $N$ projects, of which up to $M$ can be selected at each time, where $1\leqslant M<N$ . Each project is modeled as a binary-action Markov d…
Conjecturesolvedindex-policies markov-decision-processes restless-banditsarXiv posted 2 days ago
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Monotonicity and finite-limit conjecture for the PI index
PI-index monotonicity and convergence conjecture. Based on extensive numerical experience, the PI index $\nu_k^{\textup{PI}}(x_k)$ is monotone increasing and converges to a finite…
Conjectureopenindex-policies queueing-theory real-time-systemsarXiv posted 2 days ago
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Extension of finite-horizon restless-bandit results to multiple actions and total-horizon budgets
Extension conjecture. The formulation of the policy and its asymptotic optimality should extend to (i) multiple actions associated with a state, instead of only an active and a pas…
Conjectureopenasymptotic-optimality index-policies restless-banditsarXiv posted 2 days ago

Whittle's asymptotic optimality conjecture for restless multi-armed bandits