10 problems

Time-varying perturbation conjecture. Optimal regret could still be achieved using

Sparsity-dependent lower-bound conjecture. A sharper minimax lower bound should be

Let $\mathcal{S}=\mathbb{R}^{\mathcal{L}}_+$ be the set of nonnegative vectors indexed by locations $\mathcal{L}$. Consider a stochastic matching process for the two-level model an…

Let RMLP-2 be a contextual dynamic pricing method that assumes a log-concave noise distribution, and consider the simulation settings with standard Gaussian noise $F=\Phi(0,1)$ in…

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 $F$ belong to the function class $\mathcal{C}^{(m)}$. Smooth-noise regret conjecture. Within this function class, a tighter regret lower bound … can be achieved instead of … so…

Let $F$ be the unknown distribution of the market noise in the contextual dynamic pricing problem. Market-noise estimation conjecture. The estimation accuracy of $F$ is crucial for…

Let $M_L$ denote the relevant time-horizon parameter, and suppose the online learning algorithm has regret bounded by $O(\log(M_L)^2)$. The question is whether this bound is optima…

Consider the intertemporal pricing model in which customers' valuations may change over time, with policies ordered by their offered prices. Monotone-policy conjecture. Monotone pr…

Let customers have constant valuations and a common patience level. Liu–Cooper's cycle-size conjecture. Under some broad conditions, the cycle size of an optimal cyclic pricing pol…