This paper investigates the problem of synthesizing proactive defense systems in which the defender can allocate deceptive targets and modify the cost of actions for the attacker who aims to compromise security assets in this system. We model the interaction of the attacker and the system using a formal security model -- a probabilistic attack graph. By allocating fake targets/decoys, the defender aims to distract the attacker from compromising true targets. By increasing the cost of some attack actions, the defender aims to discourage the attacker from committing to certain policies and thereby improve the defense. To optimize the defense given limited decoy resources and operational constraints, we formulate the synthesis problem as a bi-level optimization problem, while the defender designs the system, in anticipation of the attacker's best response given that the attacker has disinformation about the system due to the use of deception. Though the general formulation with bi-level optimization is NP-hard, we show that under certain assumptions, the problem can be transformed into a constrained optimization problem. We proposed an algorithm to approximately solve this constrained optimization problem using a novel incentive-design method for projected gradient ascent. We demonstrate the effectiveness of the proposed method using extensive numerical experiments.

We present a differentiable formulation of rigid-body contact dynamics for objects and robots represented as compositions of convex primitives. Existing optimization-based approaches simulating contact between convex primitives rely on a bilevel formulation that separates collision detection and contact simulation. These approaches are unreliable in realistic contact simulation scenarios because isolating the collision detection problem introduces contact location non-uniqueness. Our approach combines contact simulation and collision detection into a unified single-level optimization problem. This disambiguates the collision detection problem in a physics-informed manner. Compared to previous differentiable simulation approaches, our formulation features improved simulation robustness and a reduction in computational complexity by more than an order of magnitude. We illustrate the contact and collision differentiability on a robotic manipulation task requiring optimization-through-contact. We provide a numerically efficient implementation of our formulation in the Julia language called Silico.jl.

The sixth generation (6G) wireless systems are envisioned to enable the paradigm shift from "connected things" to "connected intelligence", featured by ultra high density, large-scale, dynamic heterogeneity, diversified functional requirements and machine learning capabilities, which leads to a growing need for highly efficient intelligent algorithms. The classic optimization-based algorithms usually require highly precise mathematical model of data links and suffer from poor performance with high computational cost in realistic 6G applications. Based on domain knowledge (e.g., optimization models and theoretical tools), machine learning (ML) stands out as a promising and viable methodology for many complex large-scale optimization problems in 6G, due to its superior performance, generalizability, computational efficiency and robustness. In this paper, we systematically review the most representative "learning to optimize" techniques in diverse domains of 6G wireless networks by identifying the inherent feature of the underlying optimization problem and investigating the specifically designed ML frameworks from the perspective of optimization. In particular, we will cover algorithm unrolling, learning to branch-and-bound, graph neural network for structured optimization, deep reinforcement learning for stochastic optimization, end-to-end learning for semantic optimization, as well as federated learning for distributed optimization, for solving challenging large-scale optimization problems arising from various important wireless applications. Through the in-depth discussion, we shed light on the excellent performance of ML-based optimization algorithms with respect to the classical methods, and provide insightful guidance to develop advanced ML techniques in 6G networks.

Algorithms are becoming more capable, and with that comes hic sunt dracones (here be dragons). The term symbolizes areas beyond our known maps. We use this term since we are stepping into an exciting, potentially dangerous, and unknown area with algorithms. Our curiosity to understand the natural world drives our search for new methods. For this reason, it is crucial to explore this subject. The project's objective is to overlay the information obtained, in conjunction with the state of hardware today, to see if we can determine the likely directions for future algorithms'. Even though we slightly cover non-classical computing in this paper, our primary focus is on classical computing (i.e., digital computers). It is worth noting that non-classical quantum computing requires classical computers to operate; they are not mutually exclusive.

Humans have internal models of robots (like their physical capabilities), the world (like what will happen next), and their tasks (like a preferred goal). However, human internal models are not always perfect: for example, it is easy to underestimate a robot's inertia. Nevertheless, these models change and improve over time as humans gather more experience. Interestingly, robot actions influence what this experience is, and therefore influence how people's internal models change. In this work we take a step towards enabling robots to understand the influence they have, leverage it to better assist people, and help human models more quickly align with reality. Our key idea is to model the human's learning as a nonlinear dynamical system which evolves the human's internal model given new observations. We formulate a novel optimization problem to infer the human's learning dynamics from demonstrations that naturally exhibit human learning. We then formalize how robots can influence human learning by embedding the human's learning dynamics model into the robot planning problem. Although our formulations provide concrete problem statements, they are intractable to solve in full generality. We contribute an approximation that sacrifices the complexity of the human internal models we can represent, but enables robots to learn the nonlinear dynamics of these internal models. We evaluate our inference and planning methods in a suite of simulated environments and an in-person user study, where a 7DOF robotic arm teaches participants to be better teleoperators. While influencing human learning remains an open problem, our results demonstrate that this influence is possible and can be helpful in real human-robot interaction.

Directed information (DI) is a fundamental measure for the study and analysis of sequential stochastic models. In particular, when optimized over input distributions it characterizes the capacity of general communication channels. However, analytic computation of DI is typically intractable and existing optimization techniques over discrete input alphabets require knowledge of the channel model, which renders them inapplicable when only samples are available. To overcome these limitations, we propose a novel estimation-optimization framework for DI over discrete input spaces. We formulate DI optimization as a Markov decision process and leverage reinforcement learning techniques to optimize a deep generative model of the input process probability mass function (PMF). Combining this optimizer with the recently developed DI neural estimator, we obtain an end-to-end estimation-optimization algorithm which is applied to estimating the (feedforward and feedback) capacity of various discrete channels with memory. Furthermore, we demonstrate how to use the optimized PMF model to (i) obtain theoretical bounds on the feedback capacity of unifilar finite-state channels; and (ii) perform probabilistic shaping of constellations in the peak power-constrained additive white Gaussian noise channel.

Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only resort. We present an alternative, optimization-driven approach using tools from machine learning. We apply this approach to a novel, fully-optimizable, reaction-diffusion model which incorporates complex chemical reaction networks (termed "Dense Reaction-Diffusion Network" or "Dense RDN"). This allows us to systematically identify new states and behaviors, including pattern formation, dissipation-maximizing nonequilibrium states, and replication-like dynamical structures.

The problem of approximating the Pareto front of a multiobjective optimization problem can be reformulated as the problem of finding a set that maximizes the hypervolume indicator. This paper establishes the analytical expression of the Hessian matrix of the mapping from a (fixed size) collection of $n$ points in the $d$-dimensional decision space (or $m$ dimensional objective space) to the scalar hypervolume indicator value. To define the Hessian matrix, the input set is vectorized, and the matrix is derived by analytical differentiation of the mapping from a vectorized set to the hypervolume indicator. The Hessian matrix plays a crucial role in second-order methods, such as the Newton-Raphson optimization method, and it can be used for the verification of local optimal sets. So far, the full analytical expression was only established and analyzed for the relatively simple bi-objective case. This paper will derive the full expression for arbitrary dimensions ($m\geq2$ objective functions). For the practically important three-dimensional case, we also provide an asymptotically efficient algorithm with time complexity in $O(n\log n)$ for the exact computation of the Hessian Matrix' non-zero entries. We establish a sharp bound of $12m-6$ for the number of non-zero entries. Also, for the general $m$-dimensional case, a compact recursive analytical expression is established, and its algorithmic implementation is discussed. Also, for the general case, some sparsity results can be established; these results are implied by the recursive expression. To validate and illustrate the analytically derived algorithms and results, we provide a few numerical examples using Python and Mathematica implementations. Open-source implementations of the algorithms and testing data are made available as a supplement to this paper.

Sparse regression has been a popular approach to perform variable selection and enhance the prediction accuracy and interpretability of the resulting statistical model. Existing approaches focus on offline regularized regression, while the online scenario has rarely been studied. In this paper, we propose a novel online sparse linear regression framework for analyzing streaming data when data points arrive sequentially. Our proposed method is memory efficient and requires less stringent restricted strong convexity assumptions. Theoretically, we show that with a properly chosen regularization parameter, the $\ell_2$-norm statistical error of our estimator diminishes to zero in the optimal order of $\tilde{O}({\sqrt{s/t}})$, where $s$ is the sparsity level, $t$ is the streaming sample size, and $\tilde{O}(\cdot)$ hides logarithmic terms. Numerical experiments demonstrate the practical efficiency of our algorithm.

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic approximations of the objective function and its associated derivatives can be computed via inexact probabilistic zeroth- and first-order oracles. Under reasonable assumptions, a high-probability bound on the iteration complexity of the algorithm to approximate first-order stationarity is derived. Numerical results on standard nonlinear optimization test problems illustrate the advantages and limitations of our proposed method.