30 problems

Consider the modified version of Algorithm $\mathrm{AhdLAMulti}$ in which the dual price for the first batch is computed using only information from customers arriving in that batc…

Let $a_t$ be an independent and identically distributed process, and let $r_i$ follow either a linear regression model with white noise or a weighted random-walk model. Let $\pi_5$…

In the normal mean model, let the prior be either compactly supported or subgaussian, and consider the minimax regret over the corresponding class of priors. The previously establi…

Let $S\geq 2$ and $A\geq 2$ be integers, let $D\geq 4\left\lceil\log_A S\right\rceil$, and consider horizon-$T$ algorithms for MDPs with $S$ states, $A$ actions, and diameter at mo…

In the design-based adaptive Neyman allocation problem for augmented inverse probability weighted estimators, let $R$ denote the predictor-range parameter whose quadratic dependenc…

Let $K$ denote the number of epochs in the throughput-constrained online resource allocation model, and let the algorithm's regret be measured as a function of $K$. Regret-dependen…

The paper studies an admission-control reinforcement-learning problem with state-dependent arrival rates, and proposes an approach achieving regret bounds that improve on general u…

Let MARL denote multi-agent reinforcement learning, and let compressed environments satisfy either of the constraints referenced in the source as or. Compressed-environment regret…

Let $\mathsf{H}$ denote an upper bound on the span of the optimal bias function in an average-reward Markov decision process. In the online setting, regret is measured over the int…

In online portfolio selection, let FTRL denote Follow-the-Regularized-Leader and let LB-FTRL denote FTRL using the log-barrier regularizer. Van Erven et al.'s conjecture. FTRL with…

Low-rank tensor bandit lower-bound conjecture. The minimax regret lower bound for the low-rank tensor bandits considered in this work is

Let $T$ be the time horizon, let $d_{\max}=max_{i\in[m]}d_i$ be the largest dimension among the domains in the cascaded bandit, and let $\nu$ be the smoothness parameter of the Mat…

Consider stabilizable multidimensional linear quadratic regulator systems, and let Thompson Sampling (TS) denote an adaptive control strategy that samples a model from a posterior…

Let $D>0$, let $\mathbb{P}(\mathcal{M}^\star\in\cdot\mid H_1)$ be any prior distribution, and suppose that $\Gamma_k\leq\overline{\Gamma}$ for every $k\in[K]$. Let CVSRL denote the…

In the independent-experts setting, where each expert's gain process is independent, the continuous-time algorithm described above achieves anytime regret asymptotic to the lower b…

Van Erven and Koolen's conjecture. The dependence on $G$ in this regret bound may be merely an artifact of the analysis.

Regret lower-bound conjecture. The obtained regret upper bound is close to the lower bound for this setting. The problem is harder than standard linear bandits and dynamic pricing…

Let $M$ denote the number of stages in a multi-stage dynamic treatment regime (DTR) bandit problem, and let $T$ denote the time horizon. As $M$ becomes very large, for example comp…

The setting is online linear-quadratic tracking with prediction window $W$, horizon $N$, variation budget $L_N$, and condition number $\zeta$; the regret bounds above differ by a s…

Bounded optimality gap conjecture. Based on numerical experiments, for all $n\geq 1$ and for a large class of weight distributions,

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…

Let $\mathcal{A}$ be a generic bandit algorithm, and let $\mathcal{A}'$ be its non-restarting doubling-trick version, which reinitializes the algorithm at successive horizons while…

Let an anytime algorithm be constructed from a non-anytime algorithm by applying a doubling trick. A geometric doubling sequence is known not to preserve the relevant problem-depen…

In additive Gaussian-process Bayesian optimization, infer each additive component independently rather than using the full Gaussian process with the additive kernel. The resulting…

Improved cumulative-regret bound conjecture. The cumulative regret admits the sharper upper bound