We propose a practical sequential test for auditing differential privacy guarantees of black-box mechanisms. The test processes streams of mechanisms' outputs providing anytime-valid inference while controlling Type I error, overcoming the fixed sample size limitation of previous batch auditing methods. Experiments show this test detects violations with sample sizes that are orders of magnitude smaller than existing methods, reducing this number from 50K to a few hundred examples, across diverse realistic mechanisms. Notably, it identifies DP-SGD privacy violations in under one training run, unlike prior methods needing full model training.

Communication cost and privacy are two major considerations in federated learning (FL). For communication cost, gradient compression by sketching the clients' transmitted model updates is often used for reducing per-round communication. For privacy, the Gaussian mechanism (GM), which consists of clipping updates and adding Gaussian noise, is commonly used to guarantee client-level differential privacy. Existing literature on private FL analyzes privacy of sketching and GM in an isolated manner, illustrating that sketching provides privacy determined by the sketching dimension and that GM has to supply any additional desired privacy. In this paper, we introduce the Sketched Gaussian Mechanism (SGM), which directly combines sketching and the Gaussian mechanism for privacy.

We consider the problem of federated learning (FL) with graph-structured data distributed across multiple clients. In particular, we address the prevalent scenario of interconnected subgraphs, where interconnections between clients significantly influence the learning process. Existing approaches suffer from critical limitations, either requiring the exchange of sensitive node embeddings, thereby posing privacy risks, or relying on computationally-intensive steps, which hinders scalability. To tackle these challenges, we propose FEDLAP, a novel framework that leverages global structure information via Laplacian smoothing in the spectral domain to effectively capture inter-node dependencies while ensuring privacy and scalability. We provide a formal analysis of the privacy of FEDLAP, demonstrating that it preserves privacy. Notably, FEDLAP is the first subgraph FL scheme with strong privacy guarantees. Extensive experiments on benchmark datasets demonstrate that FEDLAP achieves competitive or superior utility compared to existing techniques.

We consider the privacy amplification properties of a sampling scheme in which a user's data is used in k steps chosen randomly and uniformly from a sequence (or set) of t steps. This sampling scheme has been recently applied in the context of differentially private optimization [Chua et al., 2024a, Choquette-Choo et al., 2025] and is also motivated by communication-efficient high-dimensional private aggregation [Asi et al., 2025]. Existing analyses of this scheme either rely on privacy amplification by shuffling which leads to overly conservative bounds or require Monte Carlo simulations that are computationally prohibitive in most practical scenarios. We give the first theoretical guarantees and numerical estimation algorithms for this sampling scheme. In particular, we demonstrate that the privacy guarantees of random k-out-of-t allocation can be upper bounded by the privacy guarantees of the well-studied independent (or Poisson) subsampling in which each step uses the user's data with probability (1+o(1))k/t. Further, we provide two additional analysis techniques that lead to numerical improvements in several parameter regimes. Altogether, our bounds give efficiently-computable and nearly tight numerical results for random allocation applied to Gaussian noise addition.

Communication cost and privacy are two major considerations in federated learning (FL). For communication cost, gradient compression by sketching the clients' transmitted model updates is often used for reducing per round communication. For privacy, the Gaussian mechanism (GM), which consists of clipping updates and adding Gaussian noise, is commonly used to guarantee client level differential privacy. Existing literature on private FL analyzes privacy of sketching and GM in an isolated manner, illustrating that sketching provides privacy determined by the sketching dimension and that GM has to supply any additional desired privacy. In this paper, we introduce the Sketched Gaussian Mechanism (SGM), which directly combines sketching and the Gaussian mechanism for privacy.

We consider the privacy amplification properties of a sampling scheme in which a user's data is used in $k$ steps chosen randomly and uniformly from a sequence (or set) of $t$ steps. This sampling scheme has been recently applied in the context of differentially private optimization [Chua et al., 2024a, Choquette-Choo et al., 2024] and is also motivated by communication-efficient high-dimensional private aggregation [Asi et al., 2025]. Existing analyses of this scheme either rely on privacy amplification by shuffling which leads to overly conservative bounds or require Monte Carlo simulations that are computationally prohibitive in most practical scenarios. We give the first theoretical guarantees and numerical estimation algorithms for this sampling scheme. In particular, we demonstrate that the privacy guarantees of random $k$-out-of-$t$ allocation can be upper bounded by the privacy guarantees of the well-studied independent (or Poisson) subsampling in which each step uses the user's data with probability $(1+o(1))k/t$. Further, we provide two additional analysis techniques that lead to numerical improvements in several parameter regimes. Altogether, our bounds give efficiently-computable and nearly tight numerical results for random allocation applied to Gaussian noise addition.

Poisson subsampling is the default sampling scheme in differentially private machine learning, largely because its unstructured randomness yields tractable privacy amplification analyses. Yet this same randomness introduces substantial participation variance: each sample appears in very different numbers of training iterations. In this work, we show that this variance is not merely a practical artifact to be tolerated, but a fundamental source of suboptimal privacy amplification. We prove that Balanced Iteration Subsampling (BIS), a structured scheme in which each sample participates in exactly a fixed number of iterations, achieves stronger privacy amplification than Poisson subsampling and is optimal at both extremes of the noise spectrum ($σ\to 0$ and $σ\to \infty$). Our analysis reveals that the privacy-noise tradeoff is governed not by maximizing randomness, but by eliminating participation variance while preserving uniform marginal participation across iterations. To translate this asymptotic theory into finite-noise guarantees, we introduce a practical near-exact Monte Carlo accountant for BIS, which removes the analytical slack of existing RDP and composition-based PLD analyses. Evaluations across more than 60 practical DP-SGD configurations show that BIS consistently outperforms Poisson subsampling in the low-noise regimes most relevant for high-utility private training, reducing the required noise multiplier by up to $9.6\%$. These results overturn the common intuition that more sampling randomness necessarily yields stronger privacy amplification: in DP-SGD, structured participation can be both more practical and more private. Our implementation is available at https://github.com/dong-xin-ao-andy/bis-mc-accountant.