Bounding privacy leakage over compositions, i.e., privacy accounting, is a key challenge in differential privacy (DP). However, the privacy parameter ($\varepsilon$ or $\delta$) is often easy to estimate but hard to bound. In this paper, we propose a new differential privacy paradigm called estimate-verify-release (EVR), which tackles the challenges of providing a strict upper bound for the privacy parameter in DP compositions by converting an *estimate* of privacy parameter into a formal guarantee. The EVR paradigm first verifies whether the mechanism meets the *estimated* privacy guarantee, and then releases the query output based on the verification result. The core component of the EVR is privacy verification. We develop a randomized privacy verifier using Monte Carlo (MC) technique. Furthermore, we propose an MC-based DP accountant that outperforms existing DP accounting techniques in terms of accuracy and efficiency. MC-based DP verifier and accountant is applicable to an important and commonly used class of DP algorithms, including the famous DP-SGD. An empirical evaluation shows the proposed EVR paradigm improves the utility-privacy tradeoff for privacy-preserving machine learning.

This paper focuses on the unsupervised clustering of large partially observed graphs. We propose a provable randomized framework in which a clustering algorithm is applied to a graphs adjacency matrix generated from a stochastic block model. A sub-matrix is constructed using random sampling, and the low rank component is found using a convex-optimization based matrix completion algorithm. The clusters are then identified based on this low rank component using a correlation based retrieval step. Additionally, a new random node sampling algorithm is presented which significantly improves upon the performance of the clustering algorithm with unbalanced data. Given a partially observed graph with adjacency matrix A \in R^{N \times N} , the proposed approach can reduce the computational complexity from O(N^2) to O(N).

We discuss the relative merits of optimistic and randomized approaches to exploration in reinforcement learning. Optimistic approaches presented in the literature apply an optimistic boost to the value estimate at each state-action pair and select actions that are greedy with respect to the resulting optimistic value function. Randomized approaches sample from among statistically plausible value functions and select actions that are greedy with respect to the random sample. Prior computational experience suggests that randomized approaches can lead to far more statistically efficient learning. We present two simple analytic examples that elucidate why this is the case. In principle, there should be optimistic approaches that fare well relative to randomized approaches, but that would require intractable computation. Optimistic approaches that have been proposed in the literature sacrifice statistical efficiency for the sake of computational efficiency. Randomized approaches, on the other hand, may enable simultaneous statistical and computational efficiency.

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low dimensional embedding, while in the other, sketching is based on random column and row sampling. Both designs are shown to bring about substantial savings in complexity and memory requirements for robust subspace learning over conventional approaches that use the full scale data. A characterization of the sample and computational complexity of both designs is derived in the context of two distinct outlier models, namely, sparse and independent outlier models. The proposed randomized approach can provably recover the correct subspace with computational and sample complexity that are almost independent of the size of the data. The results of the mathematical analysis are confirmed through numerical simulations using both synthetic and real data.