Statler: State-Maintaining Language Models for Embodied Reasoning

Large language models (LLMs) provide a promising tool that enable robots to perform complex robot reasoning tasks. However, the limited context window of contemporary LLMs makes reasoning over long time horizons difficult. Embodied tasks such as those that one might expect a household robot to perform typically require that the planner consider information acquired a long time ago (e.g., properties of the many objects that the robot previously encountered in the environment). Attempts to capture the world state using an LLM's implicit internal representation is complicated by the paucity of task- and environment-relevant information available in a robot's action history, while methods that rely on the ability to convey information via the prompt to the LLM are subject to its limited context window. In this paper, we propose Statler, a framework that endows LLMs with an explicit representation of the world state as a form of ``memory'' that is maintained over time. Integral to Statler is its use of two instances of general LLMs -- a world-model reader and a world-model writer -- that interface with and maintain the world state. By providing access to this world state ``memory'', Statler improves the ability of existing LLMs to reason over longer time horizons without the constraint of context length. We evaluate the effectiveness of our approach on three simulated table-top manipulation domains and a real robot domain, and show that it improves the state-of-the-art in LLM-based robot reasoning. Project website: https://statler-lm.github.io/

Federated Linear Contextual Bandits with User-level Differential Privacy

This paper studies federated linear contextual bandits under the notion of user-level differential privacy (DP). We first introduce a unified federated bandits framework that can accommodate various definitions of DP in the sequential decision-making setting. We then formally introduce user-level central DP (CDP) and local DP (LDP) in the federated bandits framework, and investigate the fundamental trade-offs between the learning regrets and the corresponding DP guarantees in a federated linear contextual bandits model. For CDP, we propose a federated algorithm termed as $\texttt{ROBIN}$ and show that it is near-optimal in terms of the number of clients $M$ and the privacy budget $\varepsilon$ by deriving nearly-matching upper and lower regret bounds when user-level DP is satisfied. For LDP, we obtain several lower bounds, indicating that learning under user-level $(\varepsilon,\delta)$-LDP must suffer a regret blow-up factor at least $\min\{1/\varepsilon,M\}$ or $\min\{1/\sqrt{\varepsilon},\sqrt{M}\}$ under different conditions.

DP-HyPO: An Adaptive Private Hyperparameter Optimization Framework

Hyperparameter optimization, also known as hyperparameter tuning, is a widely recognized technique for improving model performance. Regrettably, when training private ML models, many practitioners often overlook the privacy risks associated with hyperparameter optimization, which could potentially expose sensitive information about the underlying dataset. Currently, the sole existing approach to allow privacy-preserving hyperparameter optimization is to uniformly and randomly select hyperparameters for a number of runs, subsequently reporting the best-performing hyperparameter. In contrast, in non-private settings, practitioners commonly utilize "adaptive" hyperparameter optimization methods such as Gaussian process-based optimization, which select the next candidate based on information gathered from previous outputs. This substantial contrast between private and non-private hyperparameter optimization underscores a critical concern. In our paper, we introduce DP-HyPO, a pioneering framework for "adaptive" private hyperparameter optimization, aiming to bridge the gap between private and non-private hyperparameter optimization. To accomplish this, we provide a comprehensive differential privacy analysis of our framework. Furthermore, we empirically demonstrate the effectiveness of DP-HyPO on a diverse set of real-world and synthetic datasets.

Contraction of Locally Differentially Private Mechanisms

We investigate the contraction properties of locally differentially private mechanisms. More specifically, we derive tight upper bounds on the divergence between $PK$ and $QK$ output distributions of an $\epsilon$-LDP mechanism $K$ in terms of a divergence between the corresponding input distributions $P$ and $Q$, respectively. Our first main technical result presents a sharp upper bound on the $\chi^2$-divergence $\chi^2(PK\|QK)$ in terms of $\chi^2(P\|Q)$ and $\epsilon$. We also show that the same result holds for a large family of divergences, including KL-divergence and squared Hellinger distance. The second main technical result gives an upper bound on $\chi^2(PK\|QK)$ in terms of total variation distance $TV(P, Q)$ and $\epsilon$. We then utilize these bounds to establish locally private versions of the Cram\'er-Rao bound, Le Cam's, Assouad's, and the mutual information methods, which are powerful tools for bounding minimax estimation risks. These results are shown to lead to better privacy analyses than the state-of-the-arts in several statistical problems such as entropy and discrete distribution estimation, non-parametric density estimation, and hypothesis testing.

Analytical Composition of Differential Privacy via the Edgeworth Accountant

Many modern machine learning algorithms are composed of simple private algorithms; thus, an increasingly important problem is to efficiently compute the overall privacy loss under composition. In this study, we introduce the Edgeworth Accountant, an analytical approach to composing differential privacy guarantees of private algorithms. The Edgeworth Accountant starts by losslessly tracking the privacy loss under composition using the $f$-differential privacy framework, which allows us to express the privacy guarantees using privacy-loss log-likelihood ratios (PLLRs). As the name suggests, this accountant next uses the Edgeworth expansion to the upper and lower bounds the probability distribution of the sum of the PLLRs. Moreover, by relying on a technique for approximating complex distributions using simple ones, we demonstrate that the Edgeworth Accountant can be applied to the composition of any noise-addition mechanism. Owing to certain appealing features of the Edgeworth expansion, the $(\epsilon, \delta)$-differential privacy bounds offered by this accountant are non-asymptotic, with essentially no extra computational cost, as opposed to the prior approaches in, wherein the running times increase with the number of compositions. Finally, we demonstrate that our upper and lower $(\epsilon, \delta)$-differential privacy bounds are tight in federated analytics and certain regimes of training private deep learning models.

Robust Estimation for Random Graphs

We study the problem of robustly estimating the parameter $p$ of an Erd\H{o}s-R\'enyi random graph on $n$ nodes, where a $\gamma$ fraction of nodes may be adversarially corrupted. After showing the deficiencies of canonical estimators, we design a computationally-efficient spectral algorithm which estimates $p$ up to accuracy $\tilde O(\sqrt{p(1-p)}/n + \gamma\sqrt{p(1-p)} /\sqrt{n}+ \gamma/n)$ for $\gamma < 1/60$. Furthermore, we give an inefficient algorithm with similar accuracy for all $\gamma <1/2$, the information-theoretic limit. Finally, we prove a nearly-matching statistical lower bound, showing that the error of our algorithms is optimal up to logarithmic factors.

Improved Rates for Differentially Private Stochastic Convex Optimization with Heavy-Tailed Data

We study stochastic convex optimization with heavy-tailed data under the constraint of differential privacy. Most prior work on this problem is restricted to the case where the loss function is Lipschitz. Instead, as introduced by Wang, Xiao, Devadas, and Xu, we study general convex loss functions with the assumption that the distribution of gradients has bounded $k$-th moments. We provide improved upper bounds on the excess population risk under approximate differential privacy of $\tilde{O}\left(\sqrt{\frac{d}{n}}+\left(\frac{d}{\epsilon n}\right)^{\frac{k-1}{k}}\right)$ and $\tilde{O}\left(\frac{d}{n}+\left(\frac{d}{\epsilon n}\right)^{\frac{2k-2}{k}}\right)$ for convex and strongly convex loss functions, respectively. We also prove nearly-matching lower bounds under the constraint of pure differential privacy, giving strong evidence that our bounds are tight.

Robust Testing and Estimation under Manipulation Attacks

We study robust testing and estimation of discrete distributions in the strong contamination model. We consider both the "centralized setting" and the "distributed setting with information constraints" including communication and local privacy (LDP) constraints. Our technique relates the strength of manipulation attacks to the earth-mover distance using Hamming distance as the metric between messages(samples) from the users. In the centralized setting, we provide optimal error bounds for both learning and testing. Our lower bounds under local information constraints build on the recent lower bound methods in distributed inference. In the communication constrained setting, we develop novel algorithms based on random hashing and an $\ell_1/\ell_1$ isometry.

Wide Network Learning with Differential Privacy

Despite intense interest and considerable effort, the current generation of neural networks suffers a significant loss of accuracy under most practically relevant privacy training regimes. One particularly challenging class of neural networks are the wide ones, such as those deployed for NLP typeahead prediction or recommender systems. Observing that these models share something in common--an embedding layer that reduces the dimensionality of the input--we focus on developing a general approach towards training these models that takes advantage of the sparsity of the gradients. More abstractly, we address the problem of differentially private Empirical Risk Minimization (ERM) for models that admit sparse gradients. We demonstrate that for non-convex ERM problems, the loss is logarithmically dependent on the number of parameters, in contrast with polynomial dependence for the general case. Following the same intuition, we propose a novel algorithm for privately training neural networks. Finally, we provide an empirical study of a DP wide neural network on a real-world dataset, which has been rarely explored in the previous work.

Joint Design of Transmit Waveforms and Receive Filters for MIMO Radar via Manifold Optimization

The problem of joint design of transmit waveforms and receive filters is desirable in many application scenarios of multiple-input multiple-output (MIMO) radar systems. In this paper, the joint design problem is investigated under the signal-to-interference-plus-noise ratio (SINR) performance metric, in which case the problem is formulated to maximize the SINR at the receiver side subject to some practical transmit waveform constraints. A numerical algorithm is proposed for problem resolution based on the manifold optimization method, which has been shown to be powerful and flexible to address nonconvex constrained optimization problems in many engineering applications. The proposed algorithm is able to efficiently solve the SINR maximization problem with different waveform constraints under a unified framework. Numerical experiments show that the proposed algorithm outperforms the existing benchmarks in terms of computation efficiency and achieves comparable SINR performance.