Programmatically generating tight differential privacy (DP) bounds is a hard problem. Two core challenges are (1) finding expressive, compact, and efficient encodings of the distributions of DP algorithms, and (2) state space explosion stemming from the multiple quantifiers and relational properties of the DP definition. We address the first challenge by developing a method for tight privacy and accuracy bound synthesis using weighted model counting on binary decision diagrams, a state of the art technique from the artificial intelligence and automated reasoning communities for exactly computing probability distributions. We address the second challenge by developing a framework for leveraging inherent symmetries in DP algorithms. Our solution benefits from ongoing research in probabilistic programming languages, allowing us to succinctly and expressively represent different DP algorithms with approachable language syntax that can be used by non-experts. We provide a detailed case study of our solution on the binary randomized response algorithm. We also evaluate an implementation of our solution using the Dice probabilistic programming language for the randomized response and truncated geometric above threshold algorithms. We compare to prior work on exact DP verification using Markov chain probabilistic model checking and the decision procedure DiPC. Very few existing works consider mechanized analysis of accuracy guarantees for DP algorithms. We additionally provide a detailed analysis using our technique for finding tight accuracy bounds for DP algorithms.

We present a new framework for defining information leakage in the setting of US equities trading, and construct methods for deriving trading schedules that stay within specified information leakage bounds. Our approach treats the stock market as an interactive protocol performed in the presence of an adversary, and draws inspiration from the related disciplines of differential privacy as well as quantitative information flow. We apply a linear programming solver using examples from historical trade and quote (TAQ) data for US equities and describe how this framework can inform actual algorithmic trading strategies.

Probabilistic model checking is a useful technique for specifying and verifying properties of stochastic systems including randomized protocols and reinforcement learning models. However, these methods rely on the assumed structure and probabilities of certain system transitions. These assumptions may be incorrect, and may even be violated by an adversary who gains control of some system components. In this paper, we develop a formal framework for adversarial robustness in systems modeled as discrete time Markov chains (DTMCs). We base our framework on existing methods for verifying probabilistic temporal logic properties and extend it to include deterministic, memoryless policies acting in Markov decision processes (MDPs). Our framework includes a flexible approach for specifying structure-preserving and non structure-preserving adversarial models. We outline a class of threat models under which adversaries can perturb system transitions, constrained by an$\varepsilon$ball around the original transition probabilities. We define three main DTMC adversarial robustness problems: adversarial robustness verification, maximal$\delta$synthesis, and worst case attack synthesis. We present two optimization-based solutions to these three problems, leveraging traditional and parametric probabilistic model checking techniques. We then evaluate our solutions on two stochastic protocols and a collection of Grid World case studies, which model an agent acting in an environment described as an MDP. We find that the parametric solution results in fast computation for small parameter spaces. In the case of less restrictive (stronger) adversaries, the number of parameters increases, and directly computing property satisfaction probabilities is more scalable. We demonstrate the usefulness of our definitions and solutions by comparing system outcomes over various properties, threat models, and case studies.