6 problems

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Certainty-equivalence optimality conjecture for the scalar ℓ₁-gain bound
Consider the scalar positive linear-system setting above, with the certainty-equivalence (CE) policy and its certified disturbance-to-state $\ell_1$ -gain bound. CE optimality conje…
Conjectureopenadaptive-control positive-linear-systems robust-controlarXiv posted 2 days ago
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Chen's fundamental-limit conjecture for stochastic-gradient identification
Chen's conjecture. The established sufficient condition $\alpha\leq 1/3$ for strong consistency of the stochastic-gradient identification algorithm is inherently conservative; the…
Conjectureopenadaptive-control stochastic-approximation system-identificationarXiv posted 2 days ago
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Positive growth-rate conditions for robust gradient descent beyond $L_k\alpha_k>1$
Positive growth-rate conjecture. Positive growth-rate conditions on the stepsizes that allow $L_k\alpha_k>1$ should exist.
Conjectureopenadaptive-control gradient-descent optimizationarXiv posted 2 days ago
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The monitoring-function conjecture for extremum seeking with recurrent high-frequency-gain sign changes
Extremum seeking control involves an unknown plant model and objective function, and its high-frequency gain may change sign repeatedly near the optimum. A monitoring-function sche…
Conjectureopenadaptive-control extremum-seeking-control nonlinear-controlarXiv posted 2 days ago
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Uniqueness conjecture for viscosity solutions of the adaptive LQ Bellman equation
Let $U$ be the unmodified optimal cost, let $V$ be the modified optimal cost defined by … and let $f$ be a nonnegative viscosity solution of the Bellman equation. Assume that the s…
Conjectureopenadaptive-control stochastic-control viscosity-solutionsarXiv posted 2 days ago
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Lower-bound conjecture for adaptive linear-quadratic regulator regret
Let $\widehat{\pi}$ be an arbitrary adaptive policy, and let $\mathcal{R}_n(\widehat{\pi})$ denote its regret after $n$ time points. Lower-bound conjecture. For an arbitrary adapti…
Conjectureopenadaptive-control linear-quadratic-regulation regret-boundsarXiv posted 2 days ago

6 problems

Certainty-equivalence optimality conjecture for the scalar ℓ₁-gain bound

Chen's fundamental-limit conjecture for stochastic-gradient identification

Positive growth-rate conditions for robust gradient descent beyond Lkαk>1L_k\alpha_k>1Lk​αk​>1

The monitoring-function conjecture for extremum seeking with recurrent high-frequency-gain sign changes

Uniqueness conjecture for viscosity solutions of the adaptive LQ Bellman equation

Lower-bound conjecture for adaptive linear-quadratic regulator regret

Positive growth-rate conditions for robust gradient descent beyond $L_k\alpha_k>1$