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This paper considers online convex optimization with time-varying constraint functions. Specifically, we have a sequence of convex objective functions $\{f_t(x)\}_{t=0}^{\infty}$ and convex constraint functions…
Reasoning about uncertainty is vital in many real-life autonomous systems. However, current state-of-the-art planning algorithms cannot either reason about uncertainty explicitly, or do so with a high computational burden. Here, we focus on…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
Markov Decision Problems (MDPs) provide a foundational framework for modelling sequential decision-making across diverse domains, guided by optimality criteria such as discounted and average rewards. However, these criteria have inherent…
Data selection has emerged as a crucial downstream application of data valuation. While existing data valuation methods have shown promise in selection tasks, the theoretical foundations and full potential of using data values for selection…
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization…
In many use cases the execution time of tasks is unknown and can be chosen by the designer to increase or decrease the application features depending on the availability of processing capacity. If the application has real-time constraints,…
Lengthy evaluation times are common in many optimization problems such as direct policy search tasks, especially when they involve conducting evaluations in the physical world, e.g. in robotics applications. Often when evaluating solution…
We are witnessing an increasing use of data-driven predictive models to inform decisions. As decisions have implications for individuals and society, there is increasing pressure on decision makers to be transparent about their decision…
The value function plays a crucial role as a measure for the cumulative future reward an agent receives in both reinforcement learning and optimal control. It is therefore of interest to study how similar the values of neighboring states…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…
Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in larger systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression…
We propose a time value related decision function to treat a classical option pricing problem raised by Hutchinson-Lo-Poggio. In numerical experiments, the new decision function significantly improves the original model of…
Stochastic time-varying optimization is an integral part of learning in which the shape of the function changes over time in a non-deterministic manner. This paper considers multiple models of stochastic time variation and analyzes the…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Tasks that require information about the world imply a trade-off between the time spent on observation and the variance of the response. In particular, fast decisions need to rely on uncertain information. However, standard estimates of…
Deep neural networks training jobs and other iterative computations frequently include checkpoints where jobs can be canceled based on the current value of monitored metrics. While most of existing results focus on the performance of all…
We present one of the first algorithms on model based reinforcement learning and trajectory optimization with free final time horizon. Grounded on the optimal control theory and Dynamic Programming, we derive a set of backward differential…