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The Probably Approximately Correct (PAC) Privacy framework [56] provides a powerful instance-based methodology to preserve privacy in complex data-driven systems. Existing PAC Privacy algorithms (we call them Auto-PAC) rely on a Gaussian mutual information upper bound. However, we show that the upper bound obtained by Auto-PAC is tight if and only if under the data distribution, the unperturbed output is Gaussian and the noise is independent Gaussian. We propose two approaches for addressing this issue. First, we introduce two tractable post-processing methods for Auto-PAC, based on Donsker–Varadhan representation and sliced Wasserstein distances. However, the result still leaves "wasted" privacy budget. To address this issue more fundamentally, we introduce Residual-PAC (R-PAC) Privacy, an f -divergence-based measure to quantify privacy that remains after adversarial inference. To implement R-PAC Privacy in practice, we propose a Stackelberg Residual-PAC (SR-PAC) automatic privatization algorithm, a game-theoretic framework that selects optimal noise distributions through convex bilevel optimization. Our approach achieves efficient privacy budget utilization for arbitrary data distributions and naturally composes when multiple mechanisms access the dataset. Our experiments demonstrate that SR-PAC obtains consistently a better privacy-utility tradeoff than both PAC and differential privacy baselines. 

Individuals often aim to reverse undesired outcomes in interactions with automated systems, like loan denials, by either implementing system-recommended actions (recourse), or manipulating their features. While providing recourse benefits users and enhances system utility, it also provides information about the decision process that can be used for more effective strategic manipulation, especially when the individuals collectively share such information with each other. We show that this tension leads rational utility-maximizing systems to frequently withhold recourse, resulting in decreased population utility, particularly impacting sensitive groups. To mitigate these effects, we explore the role of recourse subsidies, finding them effective in increasing the provision of recourse actions by rational systems, as well as lowering the potential social cost and mitigating unfairness caused by recourse withholding. 

This paper addresses temporal logic task planning problems for mobile robots. We consider missions that require accomplishing multiple high-level sub-tasks, expressed in natural language (NL), in a temporal and logical order. To formally define the mission, we treat these sub-tasks as atomic predicates in a Linear Temporal Logic (LTL) formula. We refer to this task specification framework as LTL-NL. Our goal is to design plans, defined as sequences of robot actions, accomplishing LTL-NL tasks. This action planning problem cannot be solved directly by existing LTL planners due to the NL nature of atomic predicates. Therefore, we propose HERACLEs, a hierarchical neuro-symbolic planner that relies on a novel integration of (i) existing symbolic planners generating high-level task plans determining the order at which the NL sub-tasks should be accomplished; (ii) pre-trained Large Language Models (LLMs) to design sequences of robot actions for each sub-task in these task plans; and (iii) conformal prediction acting as a formal interface between (i) and (ii) and managing uncertainties due to LLM imperfections. We show, both theoretically and empirically, that HERACLEs can achieve user-defined mission success rates. We demonstrate the efficiency of HERACLEs through comparative numerical experiments against recent LLM-based planners as well as hardware experiments on mobile manipulation tasks. Finally, we present examples demonstrating that our approach enhances user-friendliness compared to conventional symbolic approaches.