Search

An optimal randomized strategy for design of balanced, normalized mass transport plans is developed. It replaces -- but specializes to -- the deterministic, regularized optimal transport (OT) strategy, which yields only a certainty-equivalent plan. The incompletely specified -- and therefore uncertain -- transport plan is acknowledged to be a random process. Therefore, hierarchical fully probabilistic design (HFPD) is adopted, yielding an optimal hyperprior supported on the set of possible transport plans, and consistent with prior mean constraints on the marginals of the uncertain plan. This Bayesian resetting of the design problem for transport plans -- which we call HFPD-OT -- confers new opportunities. These include (i) a strategy for the generation of a random sample of joint transport plans; (ii) randomized marginal contracts for individual source-target pairs; and (iii) consistent measures of uncertainty in the plan and its contracts. An application in algorithmic fairness is outlined, where HFPD-OT enables the recruitment of a more diverse subset of contracts -- than is possible in classical OT -- into the delivery of an expected plan. Also, it permits fairness proxies to be endowed with uncertainty quantifiers., Comment: 27 pages, 26 figures

As consumer flexibility becomes expected, it is important that the market mechanisms which attain that flexibility are perceived as fair. We set out fairness issues in energy markets today, and propose a market design to address them. Consumption is categorised as either essential or flexible with different prices and reliability levels for each. Prices are generated by an Automatic Market Maker (AMM) based on instantaneous scarcity and resource is allocated using a novel Fair Play algorithm. We empirically show the performance of the system over 1 year for 101 UK households and benchmark its performance against more classical approaches., Comment: Under review for inclusion in Special Issue of Applied Energy on `(R)Evolution of Electricity Markets: Designing Smart Electricity Markets for a Decarbonized World'

Controlled charging of electric vehicles, EVs, is a major potential source of flexibility to facilitate the integration of variable renewable energy and reduce the need for stationary energy storage. To offer system services from EVs, fleet aggregators must address the uncertainty of individual driving and charging behaviour. This paper introduces a means of forecasting the service volume available from EVs by considering several EV batteries as one conceptual battery with aggregate power and energy boundaries. This avoids the impossible task of predicting individual driving behaviour by taking advantage of the law of large numbers. The forecastability of the boundaries is demonstrated in a multiple linear regression model which achieves an $R^2$ of 0.7 for a fleet of 1,000 EVs. A two-stage stochastic model predictive control algorithm is used to schedule reserve services on a day-ahead basis addressing risk trade-offs by including Conditional Value-at-Risk in the objective function. A case study with 1.2 million domestic EV charge records from Great Britain shows that increasing fleet size improves prediction accuracy, thereby increasing reserve revenues and decreasing effective charging costs. For fleet sizes of 400 or above, charging cost reductions plateau at 60\%, with an average of 1.8kW of reserve provided per vehicle.

We present a novel class of proof-of-position algorithms: Tree-Proof-of-Position (T-PoP). This algorithm is decentralised, collaborative and can be computed in a privacy preserving manner, such that agents do not need to reveal their position publicly. We make no assumptions of honest behaviour in the system, and consider varying ways in which agents may misbehave. Our algorithm is therefore resilient to highly adversarial scenarios. This makes it suitable for a wide class of applications, namely those in which trust in a centralised infrastructure may not be assumed, or high security risk scenarios. Our algorithm has a worst case quadratic runtime, making it suitable for hardware constrained IoT applications. We also provide a mathematical model that summarises T-PoP's performance for varying operating conditions. We then simulate T-PoP's behaviour with a large number of agent-based simulations, which are in complete agreement with our mathematical model, thus demonstrating its validity. T-PoP can achieve high levels of reliability and security by tuning its operating conditions, both in high and low density environments. Finally, we also present a mathematical model to probabilistically detect platooning attacks.

Vaccination campaigns have both direct and indirect effects that act to control an infectious disease as it spreads through a population. Indirect effects arise when vaccinated individuals block disease transmission in any infection chains they are part of, and this in turn can benefit both vaccinated and unvaccinated individuals. Indirect effects are difficult to quantify in practice, but here, working with the Susceptible-Infected-Recovered (SIR) model, they are analytically calculated in important cases, through pivoting on the Final Size formula for epidemics. Their relationship to herd immunity is also clarified. Furthermore, we identify the important distinction between quantifying indirect effects of vaccination at the "population level" versus the "per capita" individual level, which often results in radically different conclusions. As an important example, the analysis unpacks why population-level indirect effect can appear significantly larger than its per capita analogue. In addition, we consider a recently proposed epidemiological non-pharamaceutical intervention used over COVID-19, referred to as "shielding", and study its impact in our mathematical analysis. The shielding scheme is extended by inclusion of limited vaccination.

Reinforcement Learning (RL) is a powerful method for controlling dynamic systems, but its learning mechanism can lead to unpredictable actions that undermine the safety of critical systems. Here, we propose RL with Adaptive Control Regularization (RL-ACR), an algorithm that enables safe RL exploration by combining the RL policy with a policy regularizer that hard-codes safety constraints. We perform policy combination via a "focus network," which determines the appropriate combination depending on the state -- relying more on the safe policy regularizer for less-exploited states while allowing unbiased convergence for well-exploited states. In a series of critical control applications, we demonstrate that RL-ACR ensures safety during training while achieving the performance standards of model-free RL approaches that disregard safety.

With the advent of the AI Act and other regulations, there is now an urgent need for algorithms that repair unfairness in training data. In this paper, we define fairness in terms of conditional independence between protected attributes ($S$) and features ($X$), given unprotected attributes ($U$). We address the important setting in which torrents of archival data need to be repaired, using only a small proportion of these data, which are $S|U$-labelled (the research data). We use the latter to design optimal transport (OT)-based repair plans on interpolated supports. This allows {\em off-sample}, labelled, archival data to be repaired, subject to stationarity assumptions. It also significantly reduces the size of the supports of the OT plans, with correspondingly large savings in the cost of their design and of their {\em sequential\/} application to the off-sample data. We provide detailed experimental results with simulated and benchmark real data (the Adult data set). Our performance figures demonstrate effective repair -- in the sense of quenching conditional dependence -- of large quantities of off-sample, labelled (archival) data.

We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove asymptotic convergence of our algorithms to a unique optimal solution. New insights obtained from the convergence proof are highlighted. An example from electrical vehicle charging in a smart city context is outlined, in which the prior zero-constraints prevent energy from being transported from some providers to some vehicles., Comment: Submitted for publication