The design of efficient nonparametric estimators has long been a central problem in statistics, machine learning, and decision making. Classical optimal procedures often rely on strong structural assumptions, which can be misspecified in practice and complicate deployment. This limitation has sparked growing interest in structure-agnostic approaches -- methods that debias black-box nuisance estimates without imposing structural priors. Understanding the fundamental limits of these methods is therefore crucial. This paper provides a systematic investigation of the optimal error rates achievable by structure-agnostic estimators. We first show that, for estimating the average treatment effect (ATE), a central parameter in causal inference, doubly robust learning attains optimal structure-agnostic error rates. We then extend our analysis to a general class of functionals that depend on unknown nuisance functions and establish the structure-agnostic optimality of debiased/double machine learning (DML). We distinguish two regimes -- one where double robustness is attainable and one where it is not -- leading to different optimal rates for first-order debiasing, and show that DML is optimal in both regimes. Finally, we instantiate our general lower bounds by deriving explicit optimal rates that recover existing results and extend to additional estimands of interest. Our results provide theoretical validation for widely used first-order debiasing methods and guidance for practitioners seeking optimal approaches in the absence of structural assumptions. This paper generalizes and subsumes the ATE lower bound established in \citet{jin2024structure} by the same authors.

We present BLINQ, a new model-based algorithm that learns the Whittle indices of an indexable, communicating and unichain Markov Decision Process (MDP). Our approach relies on building an empirical estimate of the MDP and then computing its Whittle indices using an extended version of a state-of-the-art existing algorithm. We provide a proof of convergence to the Whittle indices we want to learn as well as a bound on the time needed to learn them with arbitrary precision. Moreover, we investigate its computational complexity. Our numerical experiments suggest that BLINQ significantly outperforms existing Q-learning approaches in terms of the number of samples needed to get an accurate approximation. In addition, it has a total computational cost even lower than Q-learning for any reasonably high number of samples. These observations persist even when the Q-learning algorithms are speeded up using pre-trained neural networks to predict Q-values.

As graph-structured data grow increasingly large, evaluating their robustness under adversarial attacks becomes computationally expensive and difficult to scale. To address this challenge, we propose to compress graphs into compact representations that preserve both topological structure and robustness profile, enabling efficient and reliable evaluation. We propose Cutter, a dual-agent reinforcement learning framework composed of a Vital Detection Agent (VDA) and a Redundancy Detection Agent (RDA), which collaboratively identify structurally vital and redundant nodes for guided compression. Cutter incorporates three key strategies to enhance learning efficiency and compression quality: trajectory-level reward shaping to transform sparse trajectory returns into dense, policy-equivalent learning signals; prototype-based shaping to guide decisions using behavioral patterns from both high- and low-return trajectories; and cross-agent imitation to enable safer and more transferable exploration. Experiments on multiple real-world graphs demonstrate that Cutter generates compressed graphs that retain essential static topological properties and exhibit robustness degradation trends highly consistent with the original graphs under various attack scenarios, thereby significantly improving evaluation efficiency without compromising assessment fidelity.

However, its application to Q-learning has been limited due to the presence of the max-operator, which makes the associated ODE model a complex nonlinear system. In contrast, the associated ODE of TD learning for policy evaluation is a linear system, whose asymptotic stability is much easier to analyze in general.

We present a JIT PL semantics for ReLU-type networks that compiles models into a guarded CPWL transducer with shared guards. The system adds hyperplanes only when operands are affine on the current cell, maintains global lower/upper envelopes, and uses a budgeted branch-and-bound. We obtain anytime soundness, exactness on fully refined cells, monotone progress, guard-linear complexity (avoiding global $\binom{k}{2}$), dominance pruning, and decidability under finite refinement. The shared carrier supports region extraction, decision complexes, Jacobians, exact/certified Lipschitz, LP/SOCP robustness, and maximal causal influence. A minimal prototype returns certificates or counterexamples with cost proportional to visited subdomains.

We hereby provide a summarizing figure of the training and inference stages used in TIM. Figure 2: Outline of TIM framework (best viewed in color).