Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression

We propose an optimal algorithm for estimating conditional average treatment effects (CATEs) when response functions lie in a reproducing kernel Hilbert space (RKHS). We study settings in which the contrast function is structurally simpler than the nuisance functions: (i) it lies in a lower-complexity RKHS with faster eigenvalue decay, (ii) it satisfies a source condition relative to the nuisance kernel, or (iii) it depends on a known low-dimensional covariate representation. We develop a unified two-stage kernel ridge regression (KRR) method that attains minimax rates governed by the complexity of the contrast function rather than the nuisance class, in terms of both sample size and overlap. We also show that a simple model-selection step over candidate contrast spaces and regularization levels yields an oracle inequality, enabling adaptation to unknown CATE regularity.

Experimental Design for Semiparametric Bandits

We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in practice. We propose the first experimental-design approach that simultaneously offers a sharp regret bound, a PAC bound, and a best-arm identification guarantee. Our method attains the minimax regret $\tilde{O}(\sqrt{dT})$, matching the known lower bound for finite-armed linear bandits, and further achieves logarithmic regret under a positive suboptimality gap condition. These guarantees follow from our refined non-asymptotic analysis of orthogonalized regression that attains the optimal $\sqrt{d}$ rate, paving the way for robust and efficient learning across a broad class of semiparametric bandit problems.

Local Anti-Concentration Class: Logarithmic Regret for Greedy Linear Contextual Bandit

We study the performance guarantees of exploration-free greedy algorithms for the linear contextual bandit problem. We introduce a novel condition, named the \textit{Local Anti-Concentration} (LAC) condition, which enables a greedy bandit algorithm to achieve provable efficiency. We show that the LAC condition is satisfied by a broad class of distributions, including Gaussian, exponential, uniform, Cauchy, and Student's~$t$ distributions, along with other exponential family distributions and their truncated variants. This significantly expands the class of distributions under which greedy algorithms can perform efficiently. Under our proposed LAC condition, we prove that the cumulative expected regret of the greedy algorithm for the linear contextual bandit is bounded by $O(\operatorname{poly} \log T)$. Our results establish the widest range of distributions known to date that allow a sublinear regret bound for greedy algorithms, further achieving a sharp poly-logarithmic regret.