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We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded number of components and interactions, written using a multiplicative conjunction, reminiscent of Bunched Implications and Separation Logic. We study the complexity of the satisfiability and entailment problems for the configuration logic under consideration. Additionally, we consider robustness properties, such as tightness (are all interactions entirely connected to components?) and degree boundedness (is every component involved in a bounded number of interactions?), the latter being an ingredient for decidability of entailments.

This paper considers safe control synthesis for dynamical systems in the presence of uncertainty in the dynamics model and the safety constraints that the system must satisfy. Our approach captures probabilistic and worst-case model errors and their effect on control Lyapunov function (CLF) and control barrier function (CBF) constraints in the control-synthesis optimization problem. We show that both the probabilistic and robust formulations lead to second-order cone programs (SOCPs), enabling safe and stable control synthesis that can be performed efficiently online. We evaluate our approach in PyBullet simulations of an autonomous robot navigating in unknown environments and compare the performance with a baseline CLF-CBF quadratic programming approach.

In this work, we focus on solving a decentralized consensus problem in a private manner. Specifically, we consider a setting in which a group of nodes, connected through a network, aim at computing the mean of their local values without revealing those values to each other. The distributed consensus problem is a classic problem that has been extensively studied and its convergence characteristics are well-known. Alas, state-of-the-art consensus methods build on the idea of exchanging local information with neighboring nodes which leaks information about the users' local values. We propose an algorithmic framework that is capable of achieving the convergence limit and rate of classic consensus algorithms while keeping the users' local values private. The key idea of our proposed method is to carefully design noisy messages that are passed from each node to its neighbors such that the consensus algorithm still converges precisely to the average of local values, while a minimum amount of information about local values is leaked. We formalize this by precisely characterizing the mutual information between the private message of a node and all the messages that another adversary collects over time. We prove that our method is capable of preserving users' privacy for any network without a so-called "generalized leaf", and formalize the trade-off between privacy and convergence time. Unlike many private algorithms, any desired accuracy is achievable by our method, and the required level of privacy only affects the convergence time.

Reactive programming is a popular paradigm to program event-driven applications, and it is often proposed as a paradigm to write distributed applications. One such type of application is *prosumer* applications, which are distributed applications that both produce and consume many events. We analyse the problems that occur when using a reactive programming language or framework to implement prosumer applications. We find that the assumption of an open network, which means prosumers of various types spontaneously join and leave the network, can cause a lot of code complexity or run-time inefficiency. At the basis of these issues lies *acquaintance management*: the ability to discover prosumers as they join and leave the network, and correctly maintaining this state throughout the reactive program. Most existing reactive programming languages and frameworks have limited support for managing acquaintances, resulting in accidental complexity of the code or inefficient computations. In this paper we present acquaintance management for reactive programs. First, we design an *acquaintance discovery* mechanism to create a *flock* that automatically discovers prosumers on the network. An important aspect of flocks is their integration with reactive programs, such that a reactive program can correctly and efficiently maintain its state. To this end we design an *acquaintance maintenance* mechanism: a new type of operator for functional reactive programming languages that we call `deploy-*`. The `deploy-*` operator enables correct and efficient reactions to time-varying collections of discovered prosumers. The proposed mechanisms are implemented in a reactive programming language called Stella, which serves as a linguistic vehicle to demonstrate the ideas of our approach. Our implementation of acquaintance management results in computationally efficient and idiomatic reactive code. We evaluate our approach quantitatively via benchmarks that show that our implementation is efficient: computations will efficiently update whenever a new prosumer is discovered, or a connected prosumer is dropped. To evaluate the distributed capabilities of our prototype implementation, we implement a use-case that simulates the bike-sharing infrastructure of Brussels, and we run it on a Raspberry Pi cluster computer. We consider our work to be an important step to use functional reactive programming to build distributed systems for open networks, in other words, distributed reactive programs that involve many prosumer devices and sensors that spontaneously join and leave the network.

Motivated by the advancing computational capacity of distributed end-user equipments (UEs), as well as the increasing concerns about sharing private data, there has been considerable recent interest in machine learning (ML) and artificial intelligence (AI) that can be processed on on distributed UEs. Specifically, in this paradigm, parts of an ML process are outsourced to multiple distributed UEs, and then the processed ML information is aggregated on a certain level at a central server, which turns a centralized ML process into a distributed one, and brings about significant benefits. However, this new distributed ML paradigm raises new risks of privacy and security issues. In this paper, we provide a survey of the emerging security and privacy risks of distributed ML from a unique perspective of information exchange levels, which are defined according to the key steps of an ML process, i.e.: i) the level of preprocessed data, ii) the level of learning models, iii) the level of extracted knowledge and, iv) the level of intermediate results. We explore and analyze the potential of threats for each information exchange level based on an overview of the current state-of-the-art attack mechanisms, and then discuss the possible defense methods against such threats. Finally, we complete the survey by providing an outlook on the challenges and possible directions for future research in this critical area.

Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional. An infinite sequence of i.i.d.\ samples $(X_i,Y_i)$ are generated according to this distribution, and two terminals observe $(X_i)$ and $(Y_i)$, respectively. They are allowed to exchange $k$ bits either in oneway or interactively in order for Bob to estimate the unknown density. We show that the minimax mean square risk is order $\left(\frac{k}{\log k} \right)^{-\frac{2\beta}{d+2\beta}}$ for one-way protocols and $k^{-\frac{2\beta}{d+2\beta}}$ for interactive protocols. The logarithmic improvement is nonexistent in the parametric counterparts, and therefore can be regarded as a consequence of nonparametric nature of the problem. Moreover, a few rounds of interactions achieve the interactive minimax rate: the number of rounds can grow as slowly as the super-logarithm (i.e., inverse tetration) of $k$. The proof of the upper bound is based on a novel multi-round scheme for estimating the joint distribution of a pair of biased Bernoulli variables.

We use the augmented Lagrangian formalism to derive discontinuous Galerkin formulations for problems in nonlinear elasticity. In elasticity stress is typically a symmetric function of strain, leading to symmetric tangent stiffness matrices in Newtons method when conforming finite elements are used for discretization. By use of the augmented Lagrangian framework, we can also obtain symmetric tangent stiffness matrices in discontinuous Galerkin methods. We suggest two different approaches and give examples from plasticity and from large deformation hyperelasticity.

This paper tackles a multi-agent bandit setting where $M$ agents cooperate together to solve the same instance of a $K$-armed stochastic bandit problem. The agents are \textit{heterogeneous}: each agent has limited access to a local subset of arms and the agents are asynchronous with different gaps between decision-making rounds. The goal for each agent is to find its optimal local arm, and agents can cooperate by sharing their observations with others. While cooperation between agents improves the performance of learning, it comes with an additional complexity of communication between agents. For this heterogeneous multi-agent setting, we propose two learning algorithms, \ucbo and \AAE. We prove that both algorithms achieve order-optimal regret, which is $O\left(\sum_{i:\tilde{\Delta}_i>0} \log T/\tilde{\Delta}_i\right)$, where $\tilde{\Delta}_i$ is the minimum suboptimality gap between the reward mean of arm $i$ and any local optimal arm. In addition, a careful selection of the valuable information for cooperation, \AAE achieves a low communication complexity of $O(\log T)$. Last, numerical experiments verify the efficiency of both algorithms.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.