🤖 machine learning

MobiWave: Dispatch-Oriented Graph Wavelets and Drift-Guided Selective Optimization for Autonomous Fleet Rebalancing

The paper proposes MobiWave, a framework for autonomous fleet rebalancing that combines dispatch-oriented multi-scale graph wavelets to disentangle traffic patterns with Drift-Guided Layer-Selective Optimization to efficiently adapt policies to mobility drift while preserving stable knowledge.

Original authors: Xiao Han, Pinbo Wang, Yuanshao Zhu, Guojiang Shen, Xiangjie Kong

Published 2026-07-28

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiao Han, Pinbo Wang, Yuanshao Zhu, Guojiang Shen, Xiangjie Kong

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the conductor of a massive, invisible orchestra made of cars. In a normal city, these cars are driven by people who have their own ideas about where to go, what music they like, and when they want to take a break. But in the world of autonomous fleets, the cars are robots that listen only to the conductor's baton. The conductor's job is fleet rebalancing: moving empty cars from places where there are too many to places where there are too few, so that when a passenger hails a ride, a car is right there waiting.

The tricky part is that the city is a living, breathing thing. Traffic jams pop up like sudden thunderstorms, new roads open like fresh shortcuts, and people's habits change like the seasons. If your conductor's brain (the computer program) is stuck in the past, it might send cars into a traffic jam that doesn't exist anymore, or miss a new shortcut that could save time. The big question for scientists is: How do you teach a robot conductor to hear the city's new rhythms without forgetting the old ones, and how do you do it without having to relearn everything from scratch every time a single streetlight changes?

This is the story of MobiWave, a new system designed to help these robot fleets dance perfectly with the city's changing steps.

The Problem: The City is a Shifting Puzzle

The authors of this paper noticed two main problems that make it hard for robot fleets to stay efficient. First, the city is messy. Sometimes a huge traffic jam covers a whole neighborhood, but if you look closely, there are tiny side streets that are still free and fast. Old computer models often blur these details together, treating the whole area as "congested" and missing the hidden escape routes. Second, the city changes over time. A road might get closed for construction, or a new shopping mall might open, changing where people want to go. If you try to update the robot's brain using only the last few hours of data, it might get confused and forget the reliable rules it learned over the last few years. If you wait too long to update, the robot becomes useless because it's driving based on yesterday's map.

The Solution: A Two-Part Super-Brain

The researchers, Xiao Han and their team, built a system called MobiWave that acts like a super-brain for these fleets. It solves the problem with two clever tricks working together.

Trick 1: The "Sound Wave" Map
Imagine the city's traffic as a piece of music. Some parts are deep, slow bass notes (like the general flow of traffic across the whole city), and some parts are high-pitched, sharp notes (like a sudden accident on one specific street). Old models often mix all these notes into a muddy noise. MobiWave uses something called Graph Wavelets. Think of this as a special pair of glasses that lets the computer see the city in different "frequencies" at the same time. It can hear the deep bass of the city-wide rush hour and the sharp squeak of a local road closure without them blending together.

But seeing the notes isn't enough; you have to know which ones matter. MobiWave has a "dispatcher's ear" that listens to the music and decides: "Right now, the high-pitched local notes are the most important for finding a ride." It weighs these different layers of information so the robot knows exactly which side streets to use for rebalancing, even when the main roads are gridlocked.

Trick 2: The "Smart Update" System
The second part of the system is called DGLS (Drift-Guided Layer-Selective Optimization). This is the system's way of learning without getting amnesia. Imagine the robot's brain is a giant library with thousands of books (layers of knowledge). When the city changes, you don't need to rewrite the whole library. You just need to update a few specific chapters.

DGLS acts like a librarian who checks the city for "drift" (changes). If the librarian notices the city is changing, they don't just throw out the old books. Instead, they:

Measure the change: They check if the change actually matters for finding rides.
Pick the right pages: They only update the specific parts of the brain (layers) that are affected by the change, leaving the stable, reliable parts alone.
Test before publishing: Before the robot starts using the new knowledge, the system runs a "test drive" in a simulation. If the new plan makes things worse or breaks safety rules, the update is rejected, and the old, safe plan stays in place.

What They Found

The team tested MobiWave using real data from cities like Manhattan and Hangzhou, as well as a simulated city. They compared their system against many other methods, including some that use giant language models (like the ones that write essays or chat with you).

The results showed that MobiWave was the best at keeping cars busy and passengers happy. In the real-world tests, it reduced the time cars spent driving empty (the "empty-loaded rate") significantly more than the other methods. For example, in the Hangzhou test, it reduced the empty driving time to about 38.54%, beating the next best method by a clear margin.

They also found that their "Smart Update" system was incredibly efficient. While other methods tried to update every single part of the robot's brain (which is slow and risky), MobiWave only updated about 54% of the parameters. This means it learned faster, used less computer power, and didn't accidentally forget the old, reliable rules.

The Takeaway

The paper suggests that to keep autonomous fleets running smoothly in a changing world, we need to stop treating the city as a blurry, static picture. Instead, we need to see the fine details of traffic like distinct sound waves and update our robot drivers carefully, only changing what needs to change. MobiWave proves that by listening to the city's specific "notes" and updating the brain with surgical precision, we can keep the fleet moving efficiently, even when the city is in a constant state of flux.

Technical Summary: MobiWave

Problem Definition

The paper addresses the challenge of autonomous fleet rebalancing in urban environments where mobility conditions are non-stationary. Unlike human-driven fleets, autonomous fleets can execute platform decisions directly, shifting the optimization goal from order matching to maximizing long-term system value through fleet-wide rebalancing.

Two primary obstacles hinder reliable deployment in this setting:

Representation Ambiguity: Regional and local traffic patterns often overlap. Standard spatial aggregation methods (e.g., neighborhood aggregation) tend to blur these patterns, potentially hiding useful free-flowing side roads behind broad congestion signals, leading to suboptimal rebalancing decisions.
Model Drift and Adaptation: Urban mobility evolves due to accidents, construction, functional zone shifts, and changing travel habits. Retraining on full historical data is computationally prohibitive, while updating all model parameters on limited recent data is risky (overfitting, catastrophic forgetting) and may erase stable knowledge. Existing continual learning methods often fail to jointly measure dispatch-relevant drift, select affected layers within a resource budget, and validate updates against service constraints.

The core problem is formulated as a joint task of dispatch-critical state perception (extracting road-network information that supports rebalancing) and continual model adaptation (maintaining reliable policies under evolving conditions using limited recent data).

Methodology: MobiWave Framework

MobiWave integrates two connected modules: a Dispatch-Oriented Multi-scale Graph Wavelet module for state representation and Drift-Guided Layer-Selective Optimization (DGLS) for adaptation.

1. Dispatch-Oriented Multi-scale Graph Wavelet

This module addresses the representation challenge by separating overlapping road-network patterns across scales.

Causal Temporal Construction: The model constructs a state representation $Z_t$ using causal observations, including current zone states, multi-horizon temporal summaries (current window mean and change), periodic codes, neighborhood demand-supply gaps, and expected vehicle arrivals. This distinguishes short-lived changes from persistent imbalances without using future data.
Multi-scale Graph Wavelets: Instead of standard aggregation, the input is decomposed over multiple graph-frequency scales using localized graph wavelets. Low-frequency scales capture smooth regional trends, while high-frequency scales preserve fine-grained local changes (e.g., specific road closures) that aggregation might obscure.
Dispatch-Aware Gating: A node-wise gate mechanism dynamically weights these spectral scales based on their value for rebalancing. It computes a weight $\alpha^b_{i,t}$ for each scale $b$ at zone $i$ , considering the local fleet imbalance and external factors. This ensures the model focuses on the specific frequency components relevant to the current dispatch decision.
Action Generation: The fused scale features feed into a policy head that predicts fleet gaps and move values. These are converted into executable integer flow matrices (vehicle movements) using a masked softmax and a rounding procedure (Allocate) that ensures feasibility (adjacency constraints, fleet conservation).
Joint Training: The representation and policy are trained jointly using a loss function combining demand prediction, move return, and policy loss, with a regularization term to prevent the gating mechanism from collapsing.

2. Drift-Guided Layer-Selective Optimization (DGLS)

DGLS addresses the adaptation challenge by selectively updating the model based on drift evidence.

Dispatch-Weighted Spectral Drift Detection: DGLS measures the drift between a recent window and a reference window using Maximum Mean Discrepancy (MMD) on the scale features. Crucially, this drift is weighted by the dispatch-relevance (gate weights) of each scale, ensuring adaptation is triggered only by changes affecting fleet decisions. A hysteretic trigger prevents noise-induced updates.
Layer Selection: When drift is detected, DGLS identifies which layers to update. It scores layers based on three signals: activation drift (MMD), current gradient sensitivity, and historical importance (to protect stable knowledge). A greedy algorithm selects a subset of layers within a fixed resource budget (e.g., parameter count or FLOPs).
Drift-Aware Fast–Slow Update: To distinguish between short-term shocks and persistent changes, DGLS employs a dual-momentum optimizer. A "fast" memory reacts immediately, while a "slow" memory updates only when drift persists. The contribution of the slow memory is modulated by the persistence of the drift, preventing temporary spikes from becoming permanent knowledge.
Candidate Validation: Before deployment, candidate updates are validated against a held-out suffix of the recent data. An update is accepted only if it improves the dispatch reward on the validation set without degrading monitored service or safety constraints. If rejected, the stable model and optimizer states are restored.

Key Contributions

Problem Formulation: The authors formulate autonomous fleet rebalancing under mobility drift as a joint problem of dispatch-critical state perception and continual model adaptation.
Dispatch-Oriented Graph Wavelets: A novel module that separates road dynamics at multiple graph-frequency scales and learns scale weights specifically for demand prediction and fleet control, avoiding the blurring effects of standard aggregation.
DGLS Framework: A selective optimization method that measures dispatch-weighted spectral drift, selects affected layers within a resource budget, and utilizes a fast–slow update mechanism with candidate validation to protect stable knowledge.
Empirical Validation: Extensive experiments on real-world datasets (Manhattan, Hangzhou) and a simulated environment demonstrate the framework's effectiveness.

Experimental Results

Overall Performance: MobiWave outperforms state-of-the-art baselines (including traditional methods, deep RL, and language-model-assisted dispatch) across three datasets. It achieves the lowest empty-loaded rate (e.g., 30.22% on Manhattan vs. 32.35% for the next best) and improves operational profit.
Adaptation to Drift: Under five types of mobility drift (sudden, gradual, structural, recurring, supply-side), MobiWave (specifically the DGLS component) consistently achieves the best empty-loaded rates, outperforming the second-best method by up to 2.10 percentage points in gradual drift scenarios. It also demonstrates faster recovery and less forgetting.
Efficiency: DGLS updates only 62.22K parameters compared to 135.94K for full-model optimizers (a 54.23% reduction), while maintaining superior performance. This confirms that focused adaptation is more effective than full-model tuning.
Ablation Studies: Removing causal summaries, graph wavelets, or dispatch-aware gating degrades performance, confirming the necessity of each component. Similarly, removing importance protection or candidate validation leads to higher empty-loaded rates or service degradation, highlighting the value of the safeguards.

Significance and Claims

The paper claims that MobiWave provides a robust solution for autonomous fleet rebalancing in dynamic urban environments by aligning representation and adaptation with fleet objectives.

Representation: It demonstrates that separating graph-frequency patterns and weighting them by dispatch value is superior to standard spatial aggregation for identifying viable rebalancing routes.
Adaptation: It argues that reliable online adaptation requires more than just updating parameters; it necessitates measuring dispatch-relevant drift, selecting affected layers within a budget, and validating updates against service constraints.
Efficiency vs. Performance: The results challenge the notion that full-model updates are necessary for adaptation, showing that selective updates guided by drift evidence can achieve better performance with significantly fewer parameter updates.

The authors conclude that detected road changes must guide the choice of model components, and every candidate update must be validated against fleet outcomes to ensure reliable deployment. Future work is suggested to explore directed graphs, delayed demand, and battery constraints.