Multiple-objective sensor management and optimisation

One of the key challenges associated with exploiting modern Autonomous Vehicle technology for military surveillance tasks is the development of Sensor Management strategies which maximise the performance of the on-board Data-Fusion systems. The focus of this thesis is the development of Sensor Management algorithms which aim to optimise target tracking processes. Three principal theoretical and analytical contributions are presented which are related to the manner in which such problems are formulated and subsequently solved.Firstly, the trade-offs between optimising target tracking and other system-level objectives relating to expected operating lifetime are explored in an autonomous ground sensor scenario. This is achieved by modelling the observer trajectory control design as a probabilistic, information-theoretic, multiple-objective optimisation problem. This novel approach explores the relationships between the changes in sensor-target geometry that are induced by tracking performance measures and those relating to power consumption. This culminates in a novel observer trajectory control algorithm based onthe minimax approach.The second contribution is an analysis of the propagation of error through a limited-lookahead sensor control feedback loop. In the last decade, it has been shown that the use of such non-myopic (multiple-step) planning strategies can lead to superior performance in many Sensor Management scenarios. However, relatively little is known about the performance of strategies which use different horizon lengths. It is shown that, in the general case, planning performance is a function of the length of the horizon over which the optimisation is performed. While increasing the horizon maximises the chances of achieving global optimality, by revealing information about the substructureof the decision space, it also increases the impact of any prediction error, approximations, or unforeseen risk present within the scenario. These competing mechanisms aredemonstrated using an example tracking problem. This provides the motivation for a novel sensor control methodology that employs an adaptive length optimisation horizon. A route to selecting the optimal horizon size is proposed, based on a new non-myopic risk equilibrium which identifies the point where the two competing mechanisms are balanced.The third area of contribution concerns the development of a number of novel optimisation algorithms aimed at solving the resulting sequential decision making problems. These problems are typically solved using stochastic search methods such as Genetic Algorithms or Simulated Annealing. The techniques presented in this thesis are extensions of the recently proposed Repeated Weighted Boosting Search algorithm. In its originalform, it is only applicable to continuous, single-objective, ptimisation problems. The extensions facilitate application to mixed search spaces and Pareto multiple-objective problems. The resulting algorithms have performance comparable with Genetic Algorithm variants, and offer a number of advantages such as ease of implementation and limited tuning requirements

A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems

05031 Abstracts Collection -- Algorithms for Optimization with Incomplete Information

From 16.01.05 to 21.01.05, the Dagstuhl Seminar 05031 ``Algorithms for Optimization with Incomplete Information\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

On Control and Estimation of Large and Uncertain Systems

This thesis contains an introduction and six papers about the control and estimation of large and uncertain systems. The first paper poses and solves a deterministic version of the multiple-model estimation problem for finite sets of linear systems. The estimate is an interpolation of Kalman filter estimates. It achieves a provided energy gain bound from disturbances to the point-wise estimation error, given that the gain bound is feasible. The second paper shows how to compute upper and lower bounds for the smallest feasible gain bound. The bounds are computed via Riccati recursions. The third paper proves that it is sufficient to consider observer-based feedback in output-feedback control of linear systems with uncertain parameters, where the uncertain parameters belong to a finite set. The paper also contains an example of a discrete-time integrator with unknown gain. The fourth paper argues that the current methods for analyzing the robustness of large systems with structured uncertainty do not distinguish between sparse and dense perturbations and proposes a new robustness measure that captures sparsity. The paper also thoroughly analyzes this new measure. In particular, it proposes an upper bound that is amenable to distributed computation and valuable for control design. The fifth paper solves the problem of localized state-feedback L2 control with communication delay for large discrete-time systems. The synthesis procedure can be performed for each node in parallel. The paper combines the localized state-feedback controller with a localized Kalman filter to synthesize a localized output feedback controller that stabilizes the closed-loop subject to communication constraints. The sixth paper concerns optimal linear-quadratic team-decision problems where the team does not have access to the model. Instead, the players must learn optimal policies by interacting with the environment. The paper contains algorithms and regret bounds for the first- and zeroth-order information feedback

Statistical Machine Learning for Modeling and Control of Stochastic Structured Systems

Machine learning and its various applications have driven innovation in robotics, synthetic perception, and data analytics. The last decade especially has experienced an explosion in interest in the research and development of artificial intelligence with successful adoption and deployment in some domains. A significant force behind these advances has been an abundance of data and the evolution of simple computational models and tools with a capacity to scale up to massive learning automata. Monolithic neural networks with billions of parameters that rely on automatic differentiation are a prime example of the significant role efficient computation has had on supercharging the ability of well-established representations to extract intelligent patterns from unstructured data. Nonetheless, despite the strides taken in the digital domains of vision and natural language processing, applications of optimal control and robotics significantly trail behind and have not been able to capitalize as much on the latest trends of machine learning. This discrepancy can be explained by the limited transferability of learning concepts that rely on full differentiability to the heavily structured physical and human interaction environments, not to mention the substantial cost of data generation on real physical systems. Therefore, these factors severely limit the application scope of loosely-structured over-parameterized data-crunching machines in the mechanical realm of robot learning and control. This thesis investigates modeling paradigms of hierarchical and switching systems to tackle some of the previously highlighted issues. This research direction is motivated by insights into universal function approximation via local cooperating units and the promise of inherently regularized representations through explicit structural design. Moreover, we explore ideas from robust optimization that address model mismatch issues in statistical models and outline how related methods may be used to improve the tractability of state filtering in stochastic hybrid systems. In Chapter 2, we consider hierarchical modeling for general regression problems. The presented approach is a generative probabilistic interpretation of local regression techniques that approximate nonlinear functions through a set of local linear or polynomial units. The number of available units is crucial in such models, as it directly balances representational power with the parametric complexity. This ambiguity is addressed by using principles from Bayesian nonparametrics to formulate flexible models that adapt their complexity to the data and can potentially encompass an infinite number of components. To learn these representations, we present two efficient variational inference techniques that scale well with data and highlight the advantages of hierarchical infinite local regression models, such as dealing with non-smooth functions, mitigating catastrophic forgetting, and enabling parameter sharing and fast predictions. Finally, we validate this approach on a set of large inverse dynamics datasets and test the learned models in real-world control scenarios. Chapter 3 addresses discrete-continuous hybrid modeling and control for stochastic dynamical systems, which implies dealing with time-series data. In this scenario, we develop an automatic system identification technique that decomposes nonlinear systems into hybrid automata and leverages the resulting structure to learn switching feedback control via hierarchical reinforcement learning. In the process, we rely on an augmented closed-loop hidden Markov model architecture that captures time correlations over long horizons and provides a principled Bayesian inference framework for learning hybrid representations and filtering the hidden discrete states to apply control accordingly. Finally, we embed this structure explicitly into a novel hybrid relative entropy policy search algorithm that optimizes a set of local polynomial feedback controllers and value functions. We validate the overall switching-system perspective by benchmarking the open-loop predictive performance against popular black-box representations. We also provide qualitative empirical results for hybrid reinforcement learning on common nonlinear control tasks. In Chapter 4, we attend to a general and fundamental problem in learning for control, namely robustness in data-driven stochastic optimization. The question of sensitivity has a strong priority, given the rising popularity of embedding statistical models into stochastic control frameworks. However, data from dynamical, especially mechanical, systems is often scarce due to a high extraction cost and limited coverage of the state-action space. The result is usually poor models with narrow validity and brittle control laws, particularly in an ill-posed over-parameterized learning example. We propose to robustify stochastic control by finding the worst-case distribution over the dynamics and optimizing a corresponding robust policy that minimizes the probability of catastrophic failures. We achieve this goal by formulating a two-stage iterative minimax optimization problem that finds the most pessimistic adversary in a trust region around a nominal model and uses it to optimize a robust optimal controller. We test this approach on a set of linear and nonlinear stochastic systems and supply empirical evidence of its practicality. Finally, we provide an outlook on how similar multi-stage distributional optimization techniques can be applied in approximate filtering of stochastic switching systems in order to tackle the issue of exponential explosion in state mixture components. In summation, the individual contributions of this thesis are a collection of interconnected principles for structured and robust learning for control. Although many challenges remain ahead, this research lays a foundation for reflecting on future structured learning questions that strive to combine optimal control and statistical machine learning perspectives for the automatic decomposition and optimization of hierarchical models