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Throughput Maximization for MapReduce-Based Collaborative Computing over Energy-Harvesting Wireless Devices
Yuhang Li, Siqi Sun, Hongen Zheng, Xiaojing Chen, Shunqing Zhang, Yanzan Sun
TL;DR
The paper addresses long-term resource allocation for MapReduce collaboration over heterogeneous energy-harvesting devices with coupled computation, communication, timing, and battery constraints. It proposes DDPG-CVX, using DDPG for energy budgeting and convex optimization for remaining per-slot allocation. Simulations report throughput gains of 1.25× to 32.36× over representative benchmarks.
Problem
MapReduce-based collaborative computing over energy-harvesting devices requires joint resource allocation under heterogeneous hardware, uncertain energy arrivals, finite batteries, and time-varying channels.
Method
DDPG-CVX uses DDPG to determine per-device energy budgets and convex optimization to globally solve the remaining per-slot resource allocation.
Results
DDPG-CVX achieves 1.25×, 1.51×, 1.75×, 2.87×, and 32.36× the throughput of DDPG-only, GA, RB, AA, and MAXF, respectively.
Takeaways & Limitations
The two-phase decomposition reduces the DRL action dimension while retaining globally optimized per-slot allocation and higher throughput than DDPG alone.
Takeaways & Limitations
The convex subproblem has worst-case interior-point complexity O(N^3.5), making the stated tractability scope moderate-scale deployments.
Abstract
from arXiv · showhide
This paper studies resource allocation for MapReduce-based collaborative computing over heterogeneous wireless devices powered by renewable energy harvesting. We formulate a long-run average throughput maximization problem that jointly optimizes computing load, phase time allocations, transmit power, and per-device energy consumption, subject to battery evolution, CPU frequency, and latency constraints. To solve this problem online without prior knowledge of channel states or energy arrivals, we propose a DDPG-CVX algorithm that couples Deep Deterministic Policy Gradient (DDPG) with convex programming. DDPG determines the per-slot energy budget for each device from observed battery and channel states; the remaining resource allocation variables are then resolved to global optimality by an embedded convex solver. This two-phase decomposition reduces the action-space dimensionality of DDPG while preserving per-slot solution quality. Simulations show that DDPG-CVX achieves 1.25$\times$$\sim$32.36$\times$ the throughput of representative benchmarks.
I. INTRODUCTION
The paper targets throughput maximization for MapReduce collaboration among heterogeneous, energy-harvesting devices under coupled computation, communication, timing, and battery constraints. It proposes DDPG-CVX, which combines long-term energy planning with globally optimized per-slot allocation and outperforms the considered baselines in simulation.
- Motivation: MapReduce distributes computation across heterogeneous wireless devices through Map, Shuffle, and Reduce phases, helping resource-constrained devices execute demanding applications.The framework also accounts for computation energy, uplink transmission energy, and harvested-energy sustainability.
- Research gap: Existing approaches often assume homogeneous devices or known future conditions, while joint optimization of computing load, timing, transmit power, and energy remains underexplored.Finite batteries and uncertain energy arrivals couple current decisions with future feasibility.
- Contributions: The paper formulates long-run average throughput maximization over computing load, phase durations, transmit power, and device energy under computation, communication, latency, and battery constraints.The formulation captures temporal coupling from battery dynamics and time-varying channels.
- Contributions: DDPG-CVX assigns per-device energy budgets with DDPG and globally solves the remaining per-slot allocation through convex optimization, reducing the DRL action dimension.The decomposition is designed to enable faster convergence and higher throughput than DDPG alone.
- Results: DDPG-CVX consistently achieves higher throughput than the considered baselines across diverse battery and hardware configurations.The reported simulation comparison includes throughput gains ranging from 1.25× to 32.36× over representative benchmarks.
1) MAP:
During Map, each device processes its assigned model partition to compute intermediate values. During Shuffle, devices transmit partition-dependent intermediate results through the access point.
- 1) MAP:: Each device computes intermediate values using its assigned DL model partition θ_n,t of l_n,t bits during the Map phase.The Map function produces partial inference results for the collaborating inputs.
- 2) SHUFFLE:: The Shuffle communication load is determined by the model-partition size, linking computing assignment to inter-device transmission demand.The proportionality factor is represented by β, with α := (N − 1)β for convenience.
- 2) SHUFFLE:: During Shuffle, the access point exchanges intermediate results, and each device transmits (N − 1)βl_n,t bits to the other devices.The intermediate-result size is proportional to the assigned computing load l_n,t.
3) REDUCE:
In Reduce, each device aggregates intermediate results received from all collaborators and produces the final inference result. Reduce timing is coordinated across devices within the slot.
- 3) REDUCE:: Each device aggregates βΣ_n l_n,t bits of intermediate results received from all collaborating devices before producing its final inference result.The Reduce function is denoted by ρ_x(·) for device x.
- 3) REDUCE:: Because Reduce starts only after all devices finish Map and Shuffle, the pre-Reduce waiting time is determined by the slowest device.The system-level Map-and-Shuffle latency is represented by the maximum device latency.
- 3) REDUCE:: All devices use a common Reduce-phase latency so they can complete Reduce simultaneously at the end of the slot.The stated purpose is to conserve energy.
B. Computation, Communication and Battery Models
The model captures computation, OFDMA communication, and renewable-energy battery constraints for heterogeneous devices. Device energy use and timing are governed by CPU, transmission, reserve, and battery limitations.
- Computation: Each device processes its assigned model partition during the Map phase using device-specific CPU-cycle requirements.The partition contains l_n,t bits, and computation is performed for N input samples.
- Battery: The model accounts for computation, Shuffle transmission, and Reduce energy consumption in each slot.
- Computation: CPU frequency is bounded by each device’s maximum CPU frequency.
- Communication: During Shuffle, devices use OFDMA uplinks with transmit power bounded by pmax_n and rate determined by Shannon’s theorem.Downlink transmission time and energy are neglected; uplink bandwidth is equally assigned among devices.
- Communication: The Shuffle transmission constraint ensures that delivered bits cover all required intermediate results.Transmission energy is included in the device’s total Shuffle-phase energy.
- Battery: Renewable energy is stored in rechargeable batteries with capacity Emax, while a reserve level Eres must remain available.Harvested energy is stochastic and may come from solar, indoor light, or other ambient sources.
C. Problem Formulation
The paper formulates resource allocation as long-run average computational-throughput maximization. The objective is evaluated under stochastic channel and energy-arrival processes using a finite-horizon empirical average in simulations.
- Objective: The optimization chooses per-slot resource variables to maximize average system computational throughput.The decision set includes model-partition load and phase durations for all devices.
- Objective: The long-run time-average operator supports online allocation under unpredictable channel and energy-arrival processes.
- Evaluation: Numerical evaluation approximates the long-run objective with a finite-horizon empirical time average over T slots.
III. PROPOSED DDPG-CVX FRAMEWORK
The proposed DDPG-CVX framework separates long-term energy planning from per-slot resource allocation. DDPG selects device energy budgets, and convex optimization solves the remaining allocation globally for reward evaluation.
- Motivation: Unknown future channels and energy arrivals, together with battery coupling across slots, make direct solution of the formulation difficult.
- Motivation: Direct DDPG creates a high-dimensional action space that grows with the number of devices and hinders convergence.
- Two-phase framework: DDPG determines per-device energy budgets, while convex optimization globally solves the remaining per-slot resource allocation.The resulting throughput is used as the reward for DDPG training.
A. Proposed DDPG-Based Resource Control
The DDPG controller models resource allocation as an MDP whose actions are device energy budgets. An embedded convex solver resolves remaining variables, while training uses rewards, replay, exploration, and target networks.
- MDP formulation: The MDP state contains device battery and channel information, while the action contains per-device energy budgets.The immediate reward is based on aggregate assigned computational load with a penalty for energy-budget violations.
- MDP formulation: A fixed positive penalty is applied when a generated energy budget violates the energy-availability constraint.The penalty design avoids introducing an additional optimization bias.
- DDPG control: DDPG uses actor and critic networks with online and target versions, with target networks improving training stability.
- DDPG-CVX workflow: Given the actor’s energy budgets, convex optimization determines the remaining resource variables and produces the slot reward.The workflow then transitions the agent to the next state.
- State uncertainty: In practice, battery and channel states may be estimated because of estimation errors or delayed feedback.The paper suggests noisy-state training, history-augmented policies, or conservative energy margins for stronger uncertainty.
B. Resource Allocation via Convex Optimization
DDPG fixes per-slot device energy budgets, after which convex optimization globally solves the remaining resource allocation variables. Convex reformulation preserves feasibility and solution quality while reducing the dimensionality explored by DRL.
- Convexity verification: The substitution E_SHU,tx_n,t eliminates transmit power from the communication constraint and yields a convex formulation.The transformed communication expression combines a linear term with a concave perspective term.
- Convexity verification: Map-phase and Reduce-phase energy expressions are jointly convex in their corresponding computing-load and phase-duration variables.The Map expression has the form x^3/y^2, whose Hessian is positive semidefinite for positive variables.
- Two-phase resource allocation: DDPG generates per-slot device energy budgets, while CVX optimizes computing load, phase durations, and transmit energy globally.The decomposition avoids directly exploring all resource variables with DRL.
- Convexity verification: The per-slot subproblem is a convex program because its objective and constraints are convex after reformulating communication energy.The communication constraint uses a transmit-energy substitution and the perspective of the logarithmic function.
- Complexity: The convex subproblem has 4N + 1 variables and worst-case interior-point complexity O(N^3.5), tractable for moderate deployments.Warm starts, first-order solvers, or neural surrogates are suggested for larger systems.
IV. PERFORMANCE EVALUATION
Experiments evaluate DDPG-CVX against fixed, random, averaged, direct-DDPG, and peak-frequency baselines under heterogeneous energy and hardware settings. DDPG-CVX converges fastest and achieves the highest throughput across tested battery capacities and capacitance coefficients.
- Throughput convergence: DDPG-CVX converges to the highest throughput within 1,000 episodes, while DDPG-only converges more slowly to a lower value.The direct-DDPG baseline faces a high-dimensional action space.
- Baseline comparison: 1.25×, 1.51×, 1.75×, 2.87×, and 32.36× are DDPG-CVX’s throughput ratios over DDPG-only, GA, RB, AA, and MAXF, respectively.MAXF performs worst because continuous peak-frequency operation rapidly depletes batteries and limits communication.
- Battery capacity: DDPG-CVX achieves the highest system throughput across battery capacities from 100 to 10,000 µJ.The evaluation attributes this to jointly optimizing computing load, transmit power, and phase durations.
- Hardware heterogeneity: As the capacitance coefficient k_n increases from 0.4 to 2.4, every algorithm loses throughput, while DDPG-CVX remains highest throughout.The method redistributes CPU frequencies and computing load as each CPU cycle becomes more energy-intensive.
- Hyperparameter sensitivity: γ = 0.95 and η_a = η_c = 2×10^-3 achieve the highest throughput among the tested hyperparameter settings.The results indicate sensitivity to discount-factor and learning-rate choices.
V. CONCLUSION
The paper concludes that DDPG-CVX combines long-term energy planning with globally optimized per-slot allocation for heterogeneous energy-harvesting devices. Simulations show consistent throughput gains over the considered baselines across diverse hardware configurations.
- Conclusion: DDPG-CVX combines DDPG-based long-term energy planning with convex optimization for globally solving per-slot resource allocation.This decomposition reduces the DRL action dimension.
- Conclusion: Simulation results demonstrate consistent throughput gains over the considered baselines under diverse hardware configurations.The conclusion summarizes the reported performance across the evaluated settings.