We consider a novel queuing problem where the decision-maker must choose to accept or reject randomly arriving tasks into a no buffer queue which are processed by N identical servers. Each task has a price, which is a positive real number, and a class. Each class of task has a different price distribution, service rate, and arrives according to an inhomogenous Poisson process. The objective is to decide which tasks to accept so that the total price of tasks processed is maximised over a finite horizon. We formulate the problem using a discrete time Markov Decision Process (MDP) with a hybrid state space. We show that the optimal value function has a specific structure, which enables us to solve the hybrid MDP exactly. Moreover, we rigorously prove that as the gap between successive decision epochs grows smaller, the discrete time solution approaches the optimal solution to the original continuous time problem. To improve the scalability of our approach to a greater number of servers and task classes, we present an approximation based on state abstraction. We validate our approach on synthetic data, as well as a real financial fraud data set, which is the motivating application for this work.

Counterfactual explanations inform ways to achieve a desired outcome from a machine learning model. However, such explanations are not robust to certain real-world changes in the underlying model (e.g., retraining the model, changing hyperparameters, etc.), questioning their reliability in several applications, e.g., credit lending. In this work, we propose a novel strategy - that we call RobX - to generate robust counterfactuals for tree-based ensembles, e.g., XGBoost. Tree-based ensembles pose additional challenges in robust counterfactual generation, e.g., they have a non-smooth and non-differentiable objective function, and they can change a lot in the parameter space under retraining on very similar data. We first introduce a novel metric - that we call Counterfactual Stability - that attempts to quantify how robust a counterfactual is going to be to model changes under retraining, and comes with desirable theoretical properties. Our proposed strategy RobX works with any counterfactual generation method (base method) and searches for robust counterfactuals by iteratively refining the counterfactual generated by the base method using our metric Counterfactual Stability. We compare the performance of RobX with popular counterfactual generation methods (for tree-based ensembles) across benchmark datasets. The results demonstrate that our strategy generates counterfactuals that are significantly more robust (nearly 100% validity after actual model changes) and also realistic (in terms of local outlier factor) over existing state-of-the-art methods.

The continuous automatic calibration of musical robots is an important step toward enabling them to create accurate, reliable, and expressive performances. Several attempts have been made to achieve this using external laptops, single-board computers and off-the-shelf hardware, but these solutions have various drawbacks that preclude their use in many musical robotics contexts. This paper presents a new, custom-built embedded DSP system that is capable of up to 32 channels of high quality audio input and output, created to carry out musical information retrieval tasks on the sonic output of musical robots in real time while they are performing. The results of these analyses are continuously fed to musical robot control hardware in order to inform their performance. The design and construction of the circuit board is described, the Musical Information Retrieval (MIR)-based algorithms carried out by the board are outlined, the system's performance in representative applications are evaluated, and its various implications to the field of musical robotics and beyond are discussed. By integrating this system into new musical robots, the result is instruments that are able to `listen' to the audible results of their own actuations in real time, and continuously calibrate their actions to best represent the intentions of the programmed musical composition or live input.