LipBR Algorithm Learns Where To Move Shared Bikes Without Full Demand Data

The short version

Bike and scooter share operators reposition vehicles across a city but only see how many rides happened, not how many customers were turned away. LipBR, from Hansheng Jiang and colleagues, learns reposition policies online with censored demand. The AISTATS 2026 paper gives regret bounds that grow sublinearly even when the state space is continuous and correlated.

What the researchers did

Hansheng Jiang, Shunan Jiang, and Zuo-Jun Shen analyze infinite-horizon average-cost Markov decision processes with continuous, multi-dimensional states and censored feedback motivated by vehicle sharing networks. They prove the long-run average cost is Lipschitz in policy space, then design LipBR as a Lipschitz bandit-style learner. The work appears in Proceedings of AISTATS 2026, PMLR Volume 300, Tangier, Morocco.

What they found

The algorithm achieves high-probability regret scaling as T to the power n over n plus one, times a log T term, where n is the number of locations. A matching lower bound shows the rate is order optimal. Numerical experiments in the paper report LipBR beating baseline policies across network sizes, though readers should check the PDF plots for their own scale.

Why it matters for you

Mobility and retail networks share the same pain: censored sales hide true demand, and correlated moves make each depot depend on neighbors. A provable online policy helps teams justify reposition automation to finance and ops leaders.

What to keep in mind

Theory targets base-stock style policies in the modeled MDP class. Real cities add weather, marketing, and maintenance constraints not in the proof. This is not a commercial product launch.

Vehicle sharing is a supply chain on wheels. Bikes sit at stations until riders arrive. Demand spikes after concerts or rain. Censored feedback means you only see rides taken, not riders who walked away. That hides true demand peaks. Correlated moves mean sending bikes downtown affects uptown shortages.

Lipschitz continuity means small policy tweaks change cost in a bounded way. Bandit algorithms explore policies without trying every real world day forever. Regret measures how much extra cost you pay versus the best fixed policy in hindsight. Sublinear regret means average regret per day goes to zero over time.

Operators should simulate with their station graph before trusting online learning live. Weather and pricing promos still need human rules on top.

City fleets move vehicles at night. Empty stations lose riders. Full stations waste walks. Models must learn without seeing lost demand. Math papers prove regret bounds. Bounds guide how much data you need. Code on GitHub helps replication. Start with simulation before live tests. Pair with human caps on big moves.

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Key takeaways

Censored demand breaks classic convex inventory proofs.
Lipschitz structure enables bandit-style policy search.
Regret scales with network dimension n in a known exponent.
AISTATS 2026 publication with open GitHub companion LipBR code.
Use case story centers on vehicle sharing inventory reposition.

Sources

Primary — AISTATS 2026 / PMLR, Learning in Continuous State-Space MDPs for Network Inventory Management (2026). Regret theorem and LipBR algorithm.
Secondary — GitHub, Lipschitz-NetworkInventory implementation (2026). Code companion.