Comparing Socially-Equitable Renewable Energy Budget Allocation MDP Policies in Mature and Emerging Economies

Finding policies for Markov Decision Processes (MDPs) is a central problem in areas such as Reinforcement Learning and Operations Research. Here, we have to repeatedly choose an action that should be performed by an agent. Depending on the action and the current state of the agent, the agent collects a reward and randomly transitions into a new state. The goal is to maximize the reward in expectation over a finite time horizon of length $H$. We consider a recently introduced variant that generalizes the traditionally additive reward function in the model to a monotone submodular one, which allows for capturing a range of interesting applications. Without the stochastic component, this problem is equivalent to the Submodular Orienteering problem, where the goal is to find an $s$-$t$ walk in a directed graph maximizing a monotone submodular function under a length constraint. We present a novel LP-based algorithm for Submodular Orienteering using ideas from the Sherali-Adams hierarchy and Round-or-Cut. Our guarantees are comparable to the known quasi-polynomial time logarithmic approximation for Submodular Orienteering, but also extend to the setting of Submodular Markov Decision Processes. In the polynomial time regime, we present an $O(n^{\varepsilon})$-approximation (and $O(H^{\varepsilon})$ for Submodular MDPs) for every $\varepsilon >0$, where $n$ is the number of vertices, which was unknown even for Submodular Orienteering. Prior to our work, the best known approximation guarantee for Submodular MDPs had an approximation ratio linear in $H$. Beyond these algorithmic results, our methods reveal a trade-off between the approximation guarantee and the number of previously visited vertices on which an agent conditions its decision.

The incorporation of fairness into the distribution network (DN) planning and operation has become a key goal of recent studies. The cost of implementing fairness, denominated the price of fairness (PoF), covers the efficiency that is renounced for attaining social cohesion through fair outcomes. Locational disparity makes fairness schemes emerge to level the consumers playing field. However, fairness encompasses a range of notions. From egalitarian to merit-based criteria, various metrics are implemented as a tool for measuring equitable utility distribution. These have different mathematical complexities, from linear to non-linear programming cases, which affect their overall applicability. Hence, this study compiles the overarching fairness notions and metrics, reviewing how these affect stakeholders and the inherent mathematical optimisation in resource allocation problems. The aim is to support consistent and transparent planning and decision-making within DN operations.

Energy poverty is nearly absent from NLP-for-social-good, and the little existing work is either static retrieval/QA or relies on carbon-intensive cloud LLMs, a self-defeating "computational irony" for a humanitarian setting. We present EqGrid, a closed-loop simulation in which a low-frequency, open-weight LLM policy agent sets price and carbon bounds and targeted subsidies over a community of empirically-grounded household personas, while high-frequency multi-agent RL traders clear a continuous double auction constrained by a physical distribution grid (IEEE-33-bus with Dynamic Operating Envelopes). Our contribution is threefold and directly addresses how to measure the social impact of AI: (i) grounded personas (region-matched socio-demographics) whose load curves are checked for shape and level realism against real smart-meter data; (ii) formal energy-poverty equity metrics (Energy Burden, Gini of EB, LIHC) showing the intervention reduces burden inequality without raising net grid cost; and (iii) a compute-efficiency frontier that measures how much equity performance survives compressing the policy agent from a 235B teacher down to a sub-1B model deployable on a laptop, in estimated energy/carbon per decision. A decoupled-safety design (the LLM sets bounds; a validate-and-project grid gate executes) yields zero grid-constraint violations versus 55 under direct LLM control. On energy-poverty equity, the LLM policy lowers the Gini of energy burden to 0.305 (from 0.351) and mean burden by 28% while cutting cost (outperforming a tuned rule baseline), and a 3B-active model retains 95% of the benefit at roughly 9x lower inference energy than the teacher, with even a 0.8B on-device model retaining 92% at roughly 24x lower energy. We will release code and configs.