Source-linked AI summary
Auction-based Charging Scheduling with Deep Learning Framework for Multi-Drone Networks
MyungJae Shin, Joongheon Kim, Marco Levorato
TL;DR
Drone energy limits and mobile charging stations’ restricted capacity make charging-slot scheduling in multi-drone networks a challenge, while the needed drone-distribution information may not be known in advance. The paper uses a deep-learning-based auction to learn environmental information, and reports efficient scheduling without requiring that information during auction computation.
Problem
Mobile stations have limited charging speed and capacity, while the drone-distribution information needed for auction design is not fully characterized in advance.
Source: §I · pp. 1–2Method
A deep-learning-based auction learns monotonic virtual-transformation functions from the operating environment and uses trained networks in the charging auction.
Source: §I · p. 2, B. Overall Auction Mechanism · p. 8Results
The proposed auction enables efficient scheduling by automatically learning required knowledge, so environmental information is not required during auction computation.
Source: §VI · p. 13Takeaways & Limitations
The paper presents the approach as making effective troubleshooting possible in distributed multi-drone networks.
Source: §VI · p. 13
Abstract
from arXiv · showhide
State-of-the-art drone technologies have severe flight time limitations due to weight constraints, which inevitably lead to a relatively small amount of available energy. Therefore, frequent battery replacement or recharging is necessary in applications such as delivery, exploration, or support to the wireless infrastructure. Mobile charging stations (i.e., mobile stations with charging equipment) for outdoor ad-hoc battery charging is one of the feasible solutions to address this issue. However, the ability of these platforms to charge the drones is limited in terms of the number and charging time. This paper designs an auction-based mechanism to control the charging schedule in multi-drone setting. In this paper, charging time slots are auctioned, and their assignment is determined by a bidding process. The main challenge in developing this framework is the lack of prior knowledge on the distribution of the number of drones participating in the auction. Based on optimal second-price-auction, the proposed formulation, then, relies on deep learning algorithms to learn such distribution online. Numerical results from extensive simulations show that the proposed deep learning-based approach provides effective battery charging control in multi-drone scenarios.
I. INTRODUCTION
Drone energy limits and mobile stations’ restricted charging capacity make scheduling access among competing drones a central problem. The paper proposes an auction-based charging schedule that uses deep learning to learn environmental features online and configure a revenue-oriented auction.
I. INTRODUCTION
- Mobile charging stations address the limits of stationary service areas, but their smaller capacity restricts charging speed and the number of drones served simultaneously.These constraints motivate scheduling when multiple drones compete for a station’s services.Source: §I · p. 1
- A second-price auction awards the slot to the highest bidder at a price equal to the second-highest bid, supporting truthful bidding.The paper selects this formulation because the station lacks drones’ true values before they submit bids.Source: §I · p. 2
- The station acts as auctioneer and resource seller, while each drone privately values and bids for charging time slots.The station calculates allocation probabilities and payments, assigns the slot to the highest bidder, and collects payment.Source: §I · pp. 1–2
- Because drone-location and residual-energy distributions are not fully characterized, the paper targets learning the needed distribution from the operating environment without prior assumptions.The introduction identifies this missing system knowledge as a difficulty in applying existing auctions to distributed drone networks.Source: §I · p. 2
- Deep learning approximates the non-decreasing monotonic functions used in Myerson’s virtual-transformation step, then replaces the trained network with a virtual transformation function.The learned functions configure the proposed revenue-optimal auction.Source: §I · p. 2
- The proposed auction is described as truthful and self-configurable, automatically learning environmental features with a simple structure and small computation burden.Its adaptability is presented as useful in distributed drone scenarios with time-varying features.Source: §I · p. 2
II. RELATED WORK
Related work addresses resource allocation and scheduling through auctions, but the cited approaches leave gaps around mobile-station scheduling and prior environmental knowledge. The paper positions its deep-learning auction as learning environmental characteristics in real time with limited prior information.
II. RELATED WORK
- Earlier battery-assignment and scheduling work uses quick battery replacement and maps to stationary service stations, whereas this paper schedules charging through auctions and mobile stations.The cited prior method formulates scheduling as an integer-linear programming problem after heuristic battery assignment.Source: §II · p. 2
- A prior mobile-charging robot study considers station location but not charging scheduling; this paper uses drone valuations to prioritize access to limited charging resources.The related work notes that the number of robots may exceed station charging capacity.Source: §II · p. 3
- A distributed-computing auction assumes prior environmental knowledge, while the proposed method uses deep learning to extract required features automatically.The paper presents reduced dependence on prior knowledge as relevant to real-world distributed scenarios.Source: §II · p. 3
- A distributed train-scheduling auction maximizes auctioneer revenue but requires prior information; the proposed deep-learning auction learns environmental characteristics in real time.The paper characterizes its own approach as requiring only limited information.Source: §II · p. 3
III. CHARGING SCHEDULING MECHANISM DESIGN
The mechanism treats charging slots as auctioned resources, with the mobile station as seller and drones as buyers. It uses a Myerson-based design to allocate charging and determine payments while targeting truthful participation and station revenue.
III. CHARGING SCHEDULING MECHANISM DESIGN
- The mobile station auctions charging time slots to drones, which compete through private bids for the limited charging resource.The station receives bids, computes allocation probabilities and payments, and assigns the slot to the highest bidder.Source: §III · pp. 3–4
- A drone’s private valuation reflects charging time and its expected flight time from its current battery state.The charged energy is limited by both charging rate times scheduled duration and the drone’s remaining battery capacity.Source: §III · p. 4
- The allocation rule awards charging to the highest bidder, and the payment rule sets the winner’s charge without exceeding its private valuation.The reserve price is set to zero.Source: §III · pp. 4–5
- The proposed Myerson-based auction is designed to satisfy dominant-strategy incentive compatibility and individual rationality while optimizing auctioneer revenue.These properties encourage truthful bids and ensure bidders are not charged more than their valuations.Source: §III · pp. 4–5
- Myerson’s revenue-optimal auction depends on bidders’ valuation distributions, which the proposed approach estimates with deep learning rather than requiring in advance.The learned virtual valuation function can be updated as inputs are acquired.Source: §III · p. 5
IV. DEEP LEARNING BASED AUCTION DESIGN
The design replaces Myerson’s virtual valuation function and auction rules with trainable neural networks. It uses unsupervised learning and negative expected revenue as the training objective, without requiring the valuation distribution or ground-truth outcomes.
IV. DEEP LEARNING BASED AUCTION DESIGN
- The framework replaces Myerson’s virtual valuation function, allocation rule, and payment rule with deep-learning networks for revenue-optimal auction computation.The design is described as a variant of Myerson auctions that guarantees DSIC and IR.Source: §IV · pp. 5–6
- Bids are transformed by a trained monotonic network into virtual bids, then processed by a second-price auction with zero reserve price.The inverse virtual-valuation network converts the winner’s payment back to preserve individual rationality.Source: §IV · pp. 5–6
- The model trains without ground-truth winners or payments, using negative expected auctioneer revenue as its loss and allocation probabilities and payments as inputs.L2 regularization prevents the weights and biases from becoming excessively large.Source: §IV · p. 6
- The training process does not require environmental information about the private-valuation distribution, supporting application at mobile charging stations.The authors state that the learned parameters are determined through empirical experiments.Source: §IV · p. 6
A. Deep Learning Networks
The framework uses a monotonic network to transform bids into virtual valuations, alongside allocation and payment networks. Softmax-based allocation and the parameter k shape assignment probabilities and auctioneer revenue.
A. Deep Learning Networks
- The training algorithm’s listed objectives include expected negative revenue and L2 weight loss.The supplied algorithm fragments identify these as separate computations.Source: A. Deep Learning Networks · p. 7
- The three-layer monotonic network computes group maxima, then selects their minimum, preserving monotonicity across group, unit, and min/max-operation choices.It replaces the Myerson auction's virtual valuation function.Source: A. Deep Learning Networks · pp. 6–7
- Softmax converts transformed bids into allocation probabilities, assigning the highest probability to the highest bidder; SPA-0 excludes transformed bids at or below zero.The allocation network approximates the traditional auction's allocation rule.Source: A. Deep Learning Networks · p. 7
- Larger k improves approximation quality but reduces allocation-network smoothness and increases differences between users’ allocation probabilities.The authors state that larger k leads to higher auctioneer profits, which depend on the second-highest allocation probability.Source: A. Deep Learning Networks · p. 7
- The payment network applies ReLU to the transformed bid, excluding bids below the zero reserve price before calculating the winner’s payment.The payment is calculated from the transformed bid.Source: A. Deep Learning Networks · p. 7
B. Overall Auction Mechanism
When the mobile charging system is idle, drones privately value and bid for a charging slot. The station runs the pretrained auction networks, charges the winning drone, and allocates the slot to it.
B. Overall Auction Mechanism
- If all bids are below the zero reserve price, the station does not allocate a charging slot; otherwise, the networks calculate allocation and payment probabilities.Bids below zero are converted to zero in this SPA-0 variant.Source: B. Overall Auction Mechanism · p. 8
- The station charges the drone with the highest allocation probability and assigns it the charging slot for the duration of the slot.The next auction iteration starts after the winner leaves and the station is idle again.Source: B. Overall Auction Mechanism · p. 8
- Each drone determines its valuation using private criteria and submits a bid when an auction begins.The auction begins when the mobile charging system becomes idle.Source: B. Overall Auction Mechanism · p. 8
V. PERFORMANCE EVALUATION
The evaluation reports higher charging-station revenue than SPA-0, with revenue affected by k and drone count. It also tests false-bid payments, adaptation to changing bid distributions, charging outcomes, and learned bid transformations.
Revenue Analysis - Parameter k
- At five drones, the proposed auction’s revenue exceeds SPA-0, with the highest revenue at k = 5.Revenue gaps over SPA-0 are about 2.25, 2.26, and 2.35 for k = 1, 3, and 5, respectively.Source: §V · pp. 8–9, Figure 4 · p. 9
Statistical Analysis (Parameter k)
- With k = 3, average revenue is 8.6032, nearly 7% above SPA-0; increasing k raises revenue in the reported comparisons.The analysis also compares average, maximum, minimum, and percentile revenues, and reports higher revenue for k = 3 than k = 1 across ten validation cases.Source: Figure 5 · p. 9, §V · p. 10
Performance evaluation
- Transfer learning stabilizes the auction in approximately 100 iterations after bid distributions change, versus approximately 400 iterations from initialization.The proposed model is reported to provide higher revenue than SPA-0 in this experiment.Source: Figure 7 · p. 11, §V · p. 11
- False bids 1.2–2 times the true valuation can win but increase the bidder’s payment; at a bid near 40, payment is about 32.4915 for k = 1.The reported payment increase is at least 30% over SPA-0, and the authors conclude that the payment loss discourages false bidding.Source: Figure 6 · p. 10, §V · p. 11
- With 15 drones, the proposed schedule charges 11 without battery discharge under the experiment’s one-slot, full-charge assumption.The experiment assumes consumption of 65.5mAh per hourly time step and 1000mAh recharge when a drone wins.Source: §V · p. 11
Deep Learning Model Characteristics
- The learned φ_i transformation is non-decreasing and order-preserving, while φ_shared applies a shared transformation based on φ_i outputs.The paper reports that the learned monotonic feature holds with shared or separate weights; φ_shared outputs are larger than φ_i outputs.Source: §V · p. 12
VI. CONCLUDING REMARKS AND FUTURE WORK
The proposed deep-learning auction schedules mobile charging in distributed multi-drone networks and learns the bid distribution without complex prior knowledge. The paper reports revenue-optimality and auction properties, and identifies multiple charging stations as a direction for future work.
VI. CONCLUDING REMARKS AND FUTURE WORK
- The proposed deep-learning auction is revenue-optimal for mobile charging scheduling in distributed multi-drone networks.The reported properties include individual rationality, dominant-strategy incentive compatibility, and increased payments to false-bid drones.Source: §VI · pp. 12–13
- The auction learns the required bid distribution from payment and allocation probabilities, avoiding complex prior knowledge and environmental information in auction computation.The paper attributes this environment-independent construction to the deep-learning loss function.Source: §VI · p. 13
- Future work includes formulating, verifying, and analyzing multi-item auctions for multiple mobile charging stations.The paper also notes visual attention as a possible resource-allocation application.Source: §VI · p. 13