7 problems

Let $d$ be the dimension, let $\calA$ denote the action space, and let $\mathfrak R_T^\star(d;\calA)$ be the minimax expected regret after $T$ rounds in stochastic bandit convex op…

Unconditional logarithmic rent conjecture. The bound continues to hold when (L2)--(L4) are dropped: when the excitation is endogenous to the designer's policy, agents learn from th…

Constant-strategy nonexistence conjecture. For $n\geq 6$ experts, there is no globally asymptotically optimal adversary strategy that is constant on $\mathbb{S}_n$. The paper repor…

Non-COMB uniqueness conjecture. The non-COMB strategy $(1,0,1,0,0)$ is the only globally asymptotically optimal strategy for $n=5$ experts. The claim is supported by strong numeric…

COMB optimality conjecture. The COMB strategy is globally asymptotically optimal on $\mathbb{S}_n$ only for $n\leq 4$ experts. The paper reports strong numerical evidence against g…

Oja's linear-regret conjecture. There exists such a sequence $\boldsymbol{A}_1,\dots,\boldsymbol{A}_T$, chosen obliviously and independently of Oja's initial random vector, for whi…

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 $\pi_5$…