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Press Start to Charge: Videogaming the Online Centralized Charging Scheduling Problem

Alireza Ghahtarani, Martin Cousineau, Amir-massoud Farahmand, Jorge E. Mendoza

TL;DR

This work tackles online centralized charging scheduling for home EVs by reframing it as a gamified, interactive zero-sum-like scheduling game. It compares four input-output representations (I2M, I2S, V2M, V2S) and proves that image-based inputs with movement outputs (I2M) yield the strongest theoretical generalization guarantees, while empirically delivering superior load-balancing performance. The authors develop an algorithmic suite—oracle, re-optimization, heuristics, and learning-based policies trained on expert demonstrations and refined with DAgger—evaluated across diverse arrival patterns and a real-world Greater Montréal Area case. Results show that I2M-DAgger consistently outperforms baselines in Max-Min load imbalance and RMSE, with substantial potential economic benefits from avoided distribution-capacity costs, demonstrating the practical value of gamified online coordination for residential EV charging and broader online resource allocation problems.

Abstract

We study the online centralized charging scheduling problem (OCCSP). In this problem, a central authority must decide, in real time, when to charge dynamically arriving electric vehicles (EVs), subject to capacity limits, with the objective of balancing load across a finite planning horizon. To solve the problem, we first gamify it; that is, we model it as a game where charging blocks are placed within temporal and capacity constraints on a grid. We design heuristic policies, train learning agents with expert demonstrations, and improve them using Dataset Aggregation (DAgger). From a theoretical standpoint, we show that gamification reduces model complexity and yields tighter generalization bounds than vector-based formulations. Experiments across multiple EV arrival patterns confirm that gamified learning enhances load balancing. In particular, the image-to-movement model trained with DAgger consistently outperforms heuristic baselines, vector-based approaches, and supervised learning agents, while also demonstrating robustness in sensitivity analyses. These operational gains translate into tangible economic value. In a real-world case study for the Greater Montréal Area (Québec, Canada) using utility cost data, the proposed methods lower system costs by tens of millions of dollars per year over the prevailing practice and show clear potential to delay costly grid upgrades.

Press Start to Charge: Videogaming the Online Centralized Charging Scheduling Problem

TL;DR

This work tackles online centralized charging scheduling for home EVs by reframing it as a gamified, interactive zero-sum-like scheduling game. It compares four input-output representations (I2M, I2S, V2M, V2S) and proves that image-based inputs with movement outputs (I2M) yield the strongest theoretical generalization guarantees, while empirically delivering superior load-balancing performance. The authors develop an algorithmic suite—oracle, re-optimization, heuristics, and learning-based policies trained on expert demonstrations and refined with DAgger—evaluated across diverse arrival patterns and a real-world Greater Montréal Area case. Results show that I2M-DAgger consistently outperforms baselines in Max-Min load imbalance and RMSE, with substantial potential economic benefits from avoided distribution-capacity costs, demonstrating the practical value of gamified online coordination for residential EV charging and broader online resource allocation problems.

Abstract

We study the online centralized charging scheduling problem (OCCSP). In this problem, a central authority must decide, in real time, when to charge dynamically arriving electric vehicles (EVs), subject to capacity limits, with the objective of balancing load across a finite planning horizon. To solve the problem, we first gamify it; that is, we model it as a game where charging blocks are placed within temporal and capacity constraints on a grid. We design heuristic policies, train learning agents with expert demonstrations, and improve them using Dataset Aggregation (DAgger). From a theoretical standpoint, we show that gamification reduces model complexity and yields tighter generalization bounds than vector-based formulations. Experiments across multiple EV arrival patterns confirm that gamified learning enhances load balancing. In particular, the image-to-movement model trained with DAgger consistently outperforms heuristic baselines, vector-based approaches, and supervised learning agents, while also demonstrating robustness in sensitivity analyses. These operational gains translate into tangible economic value. In a real-world case study for the Greater Montréal Area (Québec, Canada) using utility cost data, the proposed methods lower system costs by tens of millions of dollars per year over the prevailing practice and show clear potential to delay costly grid upgrades.
Paper Structure (42 sections, 3 theorems, 51 equations, 10 figures, 1 table)

This paper contains 42 sections, 3 theorems, 51 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. The OCCSP
  4. Problem Setting
  5. State Space
  6. Action Space
  7. State Transitions
  8. Reward Function
  9. Objective
  10. Representation of the Problem
  11. Vector-based Representation of the OCCSP
  12. Videogaming the OCCSP
  13. Combinations of Inputs and Outputs
  14. The Theoretical Value of Gamification
  15. Solution Approaches
  16. ...and 27 more sections

Key Result

Lemma 1

Let us consider a CNN that uses global pooling with $C$ convolution layers whose architectural hyperparameters (number of filters, kernel sizes, strides, paddings, and pooling windows) are independent of $T$. Let $\mathcal{H}_I$ denote the set of all policies that can be implemented by such CNNs wit In particular, if the image resolution $\lambda$ (the width of the input image in pixels, i.e., t

Figures (10)

  • Figure 1: Visualization of the EV scheduling game environment
  • Figure 2: Simplified illustration of model variants based on input and output types
  • Figure 3: Row-filling heuristic
  • Figure 4: X-threshold heuristic
  • Figure 5: Optimal Trajectory
  • ...and 5 more figures

Theorems & Definitions (5)

  • Lemma 1: CNN VC term vs. MLP parameter term
  • Theorem 1: Comparison of Image vs. Vector Input Estimation Error Bounds
  • Theorem 2: Comparison of $M$-class vs. $S$-class generalization terms
  • Remark 1: Special case for our EV charging game
  • Remark 2: Max-dependence, non-i.i.d