Optimization under uncertainty is an important research field especially due to its relevance in practical applications from operations research. In the real world many parameters of an optimization problem can be uncertain, e.g. the demands, returns or traffic situations or any other parameters which are not precisely known due to measurement or rounding errors. It was shown that hedging against possible perturbations in the problem parameters is essential, since already small perturbations can lead to a large violation of the constraints [BTEGN09]. Driven by the seminal works [Soy73, KY96, BTN98, BTN99, BS04] robust optimization evolved to be one of the most popular approaches to tackle uncertainty in optimization problems by finding solutions which are worst-case optimal and feasible for all parameters of a pre-defined uncertainty set; see [BBC11, BK18, GMT14] for a literature overview. Later the classical robust optimization approach was extended to the two-stage robust optimization approach (also called adaptive robust optimization) in [BTGGN04] which has been extensively studied from then on; see e.g.

Beam parameter optimization in accelerators involves multiple, sometimes competing objectives. Condensing these individual objectives into a single figure of merit unavoidably results in a bias towards particular outcomes, in absence of prior knowledge often in a non-desired way. Finding an optimal objective definition then requires operators to iterate over many possible objective weights and definitions, a process that can take many times longer than the optimization itself. A more versatile approach is multi-objective optimization, which establishes the trade-off curve or Pareto front between objectives. Here we present the first results on multi-objective Bayesian optimization of a simulated laser-plasma accelerator. We find that multi-objective optimization reaches comparable performance to its single-objective counterparts while allowing for instant evaluation of entirely new objectives. This dramatically reduces the time required to find appropriate objective definitions for new problems. Additionally, our multi-objective, multi-fidelity method reduces the time required for an optimization run by an order of magnitude. It does so by dynamically choosing simulation resolution and box size, requiring fewer slow and expensive simulations as it learns about the Pareto-optimal solutions from fast low-resolution runs. The techniques demonstrated in this paper can easily be translated into many different computational and experimental use cases beyond accelerator optimization.

An autonomous experimentation platform in manufacturing is supposedly capable of conducting a sequential search for finding suitable manufacturing conditions for advanced materials by itself or even for discovering new materials with minimal human intervention. The core of the intelligent control of such platforms is the policy directing sequential experiments, namely, to decide where to conduct the next experiment based on what has been done thus far. Such policy inevitably trades off exploitation versus exploration and the current practice is under the Bayesian optimization framework using the expected improvement criterion or its variants. We discuss whether it is beneficial to trade off exploitation versus exploration by measuring the element and degree of surprise associated with the immediate past observation. We devise a surprise-reacting policy using two existing surprise metrics, known as the Shannon surprise and Bayesian surprise. Our analysis shows that the surprise-reacting policy appears to be better suited for quickly characterizing the overall landscape of a response surface or a design place under resource constraints. We argue that such capability is much needed for futuristic autonomous experimentation platforms. We do not claim that we have a fully autonomous experimentation platform, but believe that our current effort sheds new lights or provides a different view angle as researchers are racing to elevate the autonomy of various primitive autonomous experimentation systems.

In recent years, nonlinear model predictive control (NMPC) has been extensively used for solving automotive motion control and planning tasks. In order to formulate the NMPC problem, different coordinate systems can be used with different advantages. We propose and compare formulations for the NMPC related optimization problem, involving a Cartesian and a Frenet coordinate frame (CCF/ FCF) in a single nonlinear program (NLP). We specify costs and collision avoidance constraints in the more advantageous coordinate frame, derive appropriate formulations and compare different obstacle constraints. With this approach, we exploit the simpler formulation of opponent vehicle constraints in the CCF, as well as road aligned costs and constraints related to the FCF. Comparisons to other approaches in a simulation framework highlight the advantages of the proposed approaches.

The real-time operation of large-scale infrastructure networks requires scalable optimization capabilities. Decomposition schemes can help achieve scalability; classical decomposition approaches such as the alternating direction method of multipliers (ADMM) and distributed Newtons schemes, however, often either suffer from slow convergence or might require high degrees of communication. In this work, we present new primal decomposition schemes for solving large-scale, strongly convex QPs. These approaches have global convergence guarantees and require limited communication. We benchmark their performance against the off-the-shelf interior-point method Ipopt and against ADMM on infrastructure networks that contain up to 300,000 decision variables and constraints. Overall, we find that the proposed approaches solve problems as fast as Ipopt but with reduced communication. Moreover, we find that the proposed schemes achieve higher accuracy than ADMM approaches.

A new form of ML knowledge representation with high generalization power is developed and implemented numerically. Initial $\mathit{IN}$ attributes and $\mathit{OUT}$ class label are transformed into the corresponding Hilbert spaces by considering localized wavefunctions. A partially unitary operator optimally converting a state from $\mathit{IN}$ Hilbert space into $\mathit{OUT}$ Hilbert space is then built from an optimization problem of transferring maximal possible probability from $\mathit{IN}$ to $\mathit{OUT}$, this leads to the formulation of a new algebraic problem. Constructed Knowledge Generalizing Operator $\mathcal{U}$ can be considered as a $\mathit{IN}$ to $\mathit{OUT}$ quantum channel; it is a partially unitary rectangular matrix of the dimension $\mathrm{dim}(\mathit{OUT}) \times \mathrm{dim}(\mathit{IN})$ transforming operators as $A^{\mathit{OUT}}=\mathcal{U} A^{\mathit{IN}} \mathcal{U}^{\dagger}$. Whereas only operator $\mathcal{U}$ projections squared are observable $\left\langle\mathit{OUT}|\mathcal{U}|\mathit{IN}\right\rangle^2$ (probabilities), the fundamental equation is formulated for the operator $\mathcal{U}$ itself. This is the reason of high generalizing power of the approach; the situation is the same as for the Schr\"{o}dinger equation: we can only measure $\psi^2$, but the equation is written for $\psi$ itself.

This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem, where one can not infer the loss incurred for selecting an action from observed feedback. We also introduce a new setup named Censored Semi Bandits, where the loss incurred for selecting an action can be observed under certain conditions. Finally, we study the channel selection problem in the communication networks, where the reward for an action is only observed when no other player selects that action to play in the round. These problems find applications in many fields like healthcare, crowd-sourcing, security, adaptive resource allocation, among many others. This thesis aims to address the above-described sequential decision problems by exploiting specific structures these problems exhibit. We develop provably optimal algorithms for each of these setups with weak feedback and validate their empirical performance on different problem instances derived from synthetic and real datasets.

Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in how relevant rules are defined. The learning procedure of PLD solves the optimization problem related to the search for rules (called probabilistic laws), which have a minimal length and relatively high probability. At inference, ensembles of these rules are used for prediction. Probabilistic laws are human-readable and PLD based models are transparent and inherently interpretable. Applications of PLD include classification/clusterization/regression tasks, as well as time series analysis/anomaly detection and adaptive (robotic) control. In this paper, we outline the main principles of PLD, highlight its benefits and limitations and provide some application guidelines.

The issue of left before treatment complete (LBTC) patients is common in emergency departments (EDs). This issue represents a medico-legal risk and may cause a revenue loss. Thus, understanding the factors that cause patients to leave before treatment is complete is vital to mitigate and potentially eliminate these adverse effects. This paper proposes a framework for studying the factors that affect LBTC outcomes in EDs. The framework integrates machine learning, metaheuristic optimization, and model interpretation techniques. Metaheuristic optimization is used for hyperparameter optimization--one of the main challenges of machine learning model development. Three metaheuristic optimization algorithms are employed for optimizing the parameters of extreme gradient boosting (XGB), which are simulated annealing (SA), adaptive simulated annealing (ASA), and adaptive tabu simulated annealing (ATSA). The optimized XGB models are used to predict the LBTC outcomes for the patients under treatment in ED. The designed algorithms are trained and tested using four data groups resulting from the feature selection phase. The model with the best predictive performance is interpreted using SHaply Additive exPlanations (SHAP) method. The findings show that ATSA-XGB outperformed other mode configurations with an accuracy, area under the curve (AUC), sensitivity, specificity, and F1-score of 86.61%, 87.50%, 85.71%, 87.51%, and 86.60%, respectively. The degree and the direction of effects of each feature were determined and explained using the SHAP method.

Designing a local planner to control tractor-trailer vehicles in forward and backward maneuvering is a challenging control problem in the research community of autonomous driving systems. Considering a critical situation in the stability of tractor-trailer systems, a practical and novel approach is presented to design a non-linear MPC(NMPC) local planner for tractor-trailer autonomous vehicles in both forward and backward maneuvering. The tractor velocity and steering angle are considered to be control variables. The proposed NMPC local planner is designed to handle jackknife situations, avoiding multiple static obstacles, and path following in both forward and backward maneuvering. The challenges mentioned above are converted into a constrained problem that can be handled simultaneously by the proposed NMPC local planner. The direct multiple shooting approach is used to convert the optimal control problem(OCP) into a non-linear programming problem(NLP) that IPOPT solvers can solve in CasADi. The controller performance is evaluated through different backup and forward maneuvering scenarios in the Gazebo simulation environment in real-time. It achieves asymptotic stability in avoiding static obstacles and accurate tracking performance while respecting path constraints. Finally, the proposed NMPC local planner is integrated with an open-source autonomous driving software stack called AutowareAi.