公共政策分析

*Policy gradient* (PG) methods are a class of effective *reinforcement learning* algorithms, particularly when dealing with continuous control problems. They rely on fresh *on-policy* data, making them sample-inefficient and requiring $\mathcal{O}(\epsilon^{-2})$ trajectories to reach an $\epsilon$-approximate stationary point. A common strategy to improve efficiency is to *reuse* information from past iterations, such as previous *gradients* or *trajectories*, leading to *off-policy* PG methods. While gradient reuse has received substantial attention, leading to improved rates up to $\mathcal{O}(\epsilon^{-3/2})$, the reuse of past trajectories, although intuitive, remains largely unexplored from a theoretical perspective. In this work, we provide the first rigorous theoretical evidence that reusing past off-policy trajectories can significantly accelerate PG convergence. We propose RT-PG (Reusing Trajectories - Policy Gradient), a novel algorithm that leverages a *power mean*-corrected multiple importance weighting estimator to effectively combine on-policy and off-policy data coming from the most recent $\omega$ iterations. Through a novel analysis, we prove that RT-PG achieves a sample complexity of $\widetilde{\mathcal{O}}(\epsilon^{-2}\omega^{-1})$. When reusing *all* available past trajectories, this leads to a rate of $\widetilde{\mathcal{O}}(\epsilon^{-1})$, the best known one in the literature for PG methods. We further validate our approach empirically, demonstrating its effectiveness against baselines with state-of-the-art rates.

Mean Field Games (MFGs) provide a principled framework for modelling interactions in large population systems. However, algorithmic progress has been limited since model-free methods are high variance and exact methods scale poorly. Recent Hybrid Structural Methods (HSMs) reduce variance while maintaining tractability by leveraging low-dimensional individual state and action spaces and known transition dynamics to compute the exact expected return conditioned on Monte Carlo rollouts of common noise. However, HSMs have not been extended to partially observable settings. We propose *Recurrent Structural Policy Gradient* (RSPG), the first history-aware HSM for MFGs with public partial information. RSPG achieves an order-of-magnitude faster convergence than model-free RL methods while learning history-aware behaviour, unlike current HSMs. To facilitate research into MFGs, we also introduce MFAX, our JAX-based framework for MFGs that supports both analytic and sample-based mean-field updates.

Offline Policy Evaluation (OPE) aims to estimate the value of a target policy from historical logged data without interating with the environment, thereby assessing policy performance. In settings with network interference, individuals no longer satisfy the SUTVA assumption: an individual’s outcome is influenced not only by their own treatment but also by the treatments of their neighbors, which makes the definition and estimation of policy value more complex. To capture this interference mechanism, we allow all neighbors to affect individual outcomes through a unified exposure mapping, and we use a decaying higher-order neighborhood aggregation to characterize the influence of more distant neighbors. Moreover, in real-world applications, the target policy and the logging policy often do not fully overlap (non-overlap), so the policy value in non-overlap regions cannot be point-identified. To address this issue, we partially identify the policy value over non-overlap regions and, under a smoothness assumption, formulate the estimation of the lower and upper bounds as a linear program, yielding valid bounds on the offline policy value. Finally, we conduct systematic experiments on semi-synthetic network data to validate the effectiveness and robustness of the proposed method under network interference and limited overlap.

While Randomized controlled trials (RCTs), or A/B tests, are the gold standard for optimizing online-platform policies, they are limited by discrete testing levels. This approach is suboptimal for continuous variables (e.g., prices and incentives), as it fails to extrapolate to untested values or account for user heterogeneity. We address this by developing Deep Learning for Policy Targeting (\textsf{DLPT}) to learn personalized continuous policies from discrete RCTs using high-dimensional features. We prove our estimators are asymptotically unbiased and consistent, achieving a $\sqrt{n}$-regret bound. In a collaboration with a leading social media platform to optimize creator incentives, we show that \textsf{DLPT} substantially outperforms existing benchmarks.

Noise-based certified machine unlearning currently faces a hard ceiling: the noise magnitude required to certify unlearning typically destroys model utility, particularly for large-scale deletion requests. While leveraging public data is a standard technique in differential privacy to relax this tension, its role in unlearning remains unexplored. We address this gap by introducing **Asymmetric Langevin Unlearning (ALU)**, a framework that uses public data to mitigate privacy costs. We prove that public data injection suppresses the unlearning cost by a factor of $O(1/n_{\mathrm{pub}}^2)$, guaranteeing a strict computational advantage over retraining. This establishes a new control mechanism: practitioners can mitigate the need for high noise—and the associated utility loss—by increasing the volume of public data. Crucially, we analyze the realistic setting of **distribution mismatch**, explicitly characterizing how shifts between public and private sources impact utility. We show that ALU enables "mass unlearning'' of constant dataset fractions -- a regime where standard symmetric methods become impractical -- while maintaining high utility. Empirical evaluations using variational Rényi divergence and membership inference attacks confirm that ALU effectively thwarts privacy attacks while preserving utility under reasonable distribution shifts.