This paper presents a new approach to Model Predictive Control for environments where essential, discrete variables are partially observed. Under this assumption, the belief state is a probability distribution over a finite number of states. We optimize a \textit{control-tree} where each branch assumes a given state-hypothesis. The control-tree optimization uses the probabilistic belief state information. This leads to policies more optimized with respect to likely states than unlikely ones, while still guaranteeing robust constraint satisfaction at all times. We apply the method to both linear and non-linear MPC with constraints. The optimization of the \textit{control-tree} is decomposed into optimization subproblems that are solved in parallel leading to good scalability for high number of state-hypotheses. We demonstrate the real-time feasibility of the algorithm on two examples and show the benefits compared to a classical MPC scheme optimizing w.r.t. one single hypothesis.

In earthquake-prone zones, the seismic performance of reinforced concrete cantilever (RCC) retaining walls is significant. In this study, the seismic performance was investigated using horizontal and vertical pseudo-static coefficients. To tackle RCC weights and forces resulting from these earth pressures, 26 constraints for structural strengths and geotechnical stability along with 12 geometric variables are associated with each design. These constraints and design variables form a constraint optimization problem with a twelve-dimensional solution space. To conduct effective search and produce sustainable, economical, lightweight RCC designs robust against earthquake hazards, a novel adaptive fuzzy-based metaheuristic algorithm is applied. The proposed method divides the search space to sub-regions and establishes exploration, information sharing, and exploitation search capabilities based on its novel search components. Further, fuzzy inference systems were employed to address parameterization and computational cost evaluation issues. It was found that the proposed algorithm can achieve low-cost, low-weight, and low CO2 emission RCC designs under nine seismic conditions in comparison with several classical and best-performing design optimizers.

We introduce the Blackwell discount factor for Markov Decision Processes (MDPs). Classical objectives for MDPs include discounted, average, and Blackwell optimality. Many existing approaches to computing average-optimal policies solve for discounted optimal policies with a discount factor close to $1$, but they only work under strong or hard-to-verify assumptions such as ergodicity or weakly communicating MDPs. In this paper, we show that when the discount factor is larger than the Blackwell discount factor $\gamma_{\mathrm{bw}}$, all discounted optimal policies become Blackwell- and average-optimal, and we derive a general upper bound on $\gamma_{\mathrm{bw}}$. The upper bound on $\gamma_{\mathrm{bw}}$ provides the first reduction from average and Blackwell optimality to discounted optimality, without any assumptions, and new polynomial-time algorithms for average- and Blackwell-optimal policies. Our work brings new ideas from the study of polynomials and algebraic numbers to the analysis of MDPs. Our results also apply to robust MDPs, enabling the first algorithms to compute robust Blackwell-optimal policies.

Many practical applications of robotics require systems that can operate safely despite uncertainty. In the context of motion planning, two types of uncertainty are particularly important when planning safe robot trajectories. The first is environmental uncertainty -- uncertainty in the locations of nearby obstacles, stemming from sensor noise or (in the case of obstacles' future locations) prediction error. The second class of uncertainty is uncertainty in the robots own state, typically caused by tracking or estimation error. To achieve high levels of safety, it is necessary for robots to consider both of these sources of uncertainty. In this paper, we propose a risk-bounded trajectory optimization algorithm, known as Sequential Convex Optimization with Risk Optimization (SCORA), to solve chance-constrained motion planning problems despite both environmental uncertainty and tracking error. Through experiments in simulation, we demonstrate that SCORA significantly outperforms state-of-the-art risk-aware motion planners both in planning time and in the safety of the resulting trajectories.

Cutting planes (cuts) are important for solving mixed-integer linear programs (MILPs), which formulate a wide range of important real-world applications. Cut selection -- which aims to select a proper subset of the candidate cuts to improve the efficiency of solving MILPs -- heavily depends on (P1) which cuts should be preferred, and (P2) how many cuts should be selected. Although many modern MILP solvers tackle (P1)-(P2) by manually designed heuristics, machine learning offers a promising approach to learn more effective heuristics from MILPs collected from specific applications. However, many existing learning-based methods focus on learning which cuts should be preferred, neglecting the importance of learning the number of cuts that should be selected. Moreover, we observe from extensive empirical results that (P3) what order of selected cuts should be preferred has a significant impact on the efficiency of solving MILPs as well. To address this challenge, we propose a novel hierarchical sequence model (HEM) to learn cut selection policies via reinforcement learning. Specifically, HEM consists of a two-level model: (1) a higher-level model to learn the number of cuts that should be selected, (2) and a lower-level model -- that formulates the cut selection task as a sequence to sequence learning problem -- to learn policies selecting an ordered subset with the size determined by the higher-level model. To the best of our knowledge, HEM is the first method that can tackle (P1)-(P3) in cut selection simultaneously from a data-driven perspective. Experiments show that HEM significantly improves the efficiency of solving MILPs compared to human-designed and learning-based baselines on both synthetic and large-scale real-world MILPs, including MIPLIB 2017. Moreover, experiments demonstrate that HEM well generalizes to MILPs that are significantly larger than those seen during training.

The higher speed, scalability and parallelism offered by ReRAM crossbar arrays foster development of ReRAM-based next generation AI accelerators. At the same time, sensitivity of ReRAM to temperature variations decreases R_on/Roff ratio and negatively affects the achieved accuracy and reliability of the hardware. Various works on temperature-aware optimization and remapping in ReRAM crossbar arrays reported up to 58\% improvement in accuracy and 2.39$\times$ ReRAM lifetime enhancement. This paper classifies the challenges caused by thermal heat, starting from constraints in ReRAM cells' dimensions and characteristics to their placement in the architecture. In addition, it reviews available solutions designed to mitigate the impact of these challenges, including emerging temperature-resilient DNN training methods. Our work also provides a summary of the techniques and their advantages and limitations.

We propose a new stochastic primal-dual optimization algorithm for planning in a large discounted Markov decision process with a generative model and linear function approximation. Assuming that the feature map approximately satisfies standard realizability and Bellman-closedness conditions and also that the feature vectors of all state-action pairs are representable as convex combinations of a small core set of state-action pairs, we show that our method outputs a near-optimal policy after a polynomial number of queries to the generative model. Our method is computationally efficient and comes with the major advantage that it outputs a single softmax policy that is compactly represented by a low-dimensional parameter vector, and does not need to execute computationally expensive local planning subroutines in runtime. Keywords: Markov decision processes, Linear Programming, Linear function approximation, Planning with a generative model.

Molecular dynamics aims at simulating the physical movement of atoms in order to sample the Boltzmann-Gibbs probability measure and the associated trajectories, and to compute macroscopic properties using Monte Carlo estimates [17, 1]. One of the main difficulties when performing these numerical simulations is metastability: the system tends to stay trapped in some regions of the phase space, typically in the vicinity of local maxima of the target probability measure. In this context, transitions from one metastable state to another one are of particular interest in complex systems, as they characterize for example crystallisation or enzymatic reactions. These reactions happen on a long time scale compared to the molecular timescale, so that the simulation of realistic rare events is computationally difficult. On the one hand, many efforts have been devoted to the development of rare events sampling methods in molecular dynamics. The goal of these methods is to characterize transition paths and to compute associated transition rates and mean transition times; see for instance [21] for a review. The most notable methods can be classified in two groups: (i) importance sampling techniques, where the dynamics is biased (by modifying the potential for instance) to reduce the variance of Monte Carlo estimators when computing expectations, see for instance [16, 8] for more details, and also [31, Section 6.2]. It is possible to use adaptive importance sampling strategies to choose the importance function, see [30, Chapter 5]. Another viewpoint is offered by the framework of stochastic control, as in [21] where the modification in the drift of the dynamics is determined by the solution of an optimal control problem.

The continuous computational power growth in the last decades has made solving several optimization problems significant to humankind a tractable task; however, tackling some of them remains a challenge due to the overwhelming amount of candidate solutions to be evaluated, even by using sophisticated algorithms. In such a context, a set of nature-inspired stochastic methods, called meta-heuristic optimization, can provide robust approximate solutions to different kinds of problems with a small computational burden, such as derivative-free real function optimization. Nevertheless, these methods may converge to inadequate solutions if the function landscape is too harsh, e.g., enclosing too many local optima. Previous works addressed this issue by employing a hypercomplex representation of the search space, like quaternions, where the landscape becomes smoother and supposedly easier to optimize. Under this approach, meta-heuristic computations happen in the hypercomplex space, whereas variables are mapped back to the real domain before function evaluation. Despite this latter operation being performed by the Euclidean norm, we have found that after the optimization procedure has finished, it is usually possible to obtain even better solutions by employing the Minkowski $p$-norm instead and fine-tuning $p$ through an auxiliary sub-problem with neglecting additional cost and no hyperparameters. Such behavior was observed in eight well-established benchmarking functions, thus fostering a new research direction for hypercomplex meta-heuristic optimization.

Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust optimization (DRO), and regularization. However, two issues have to be raised: 1) All these methods are biased estimators of the true optimal cost; 2) the prior distribution in the Bayesian method, the radius of the distributional ball in the DRO method, and the regularizer in the regularization method are difficult to specify. This paper studies a new framework that unifies the three approaches and that addresses the two challenges mentioned above. The asymptotic properties (e.g., consistency and asymptotic normalities), non-asymptotic properties (e.g., unbiasedness and generalization error bound), and a Monte--Carlo-based solution method of the proposed model are studied. The new model reveals the trade-off between the robustness to the unseen data and the specificity to the training data.