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TACT: A Transfer Actor-Critic Learning Framework for Energy Saving in Cellular Radio Access Networks

Rongpeng Li, Zhifeng Zhao, Xianfu Chen, Jacques Palicot, Honggang Zhang

arXiv:1211.6616v3cs.NIcs.AIcs.ITcs.LGmath.IT

TL;DR

Reliable traffic-load forecasts are challenging, and reinforcement learning may take time to converge for BS switching. The paper models the problem with reinforcement learning and transfers actor-critic knowledge from related periods or regions. Simulations report effective, robust energy-saving performance, and TACT outperforms classical actor-critic.

  • Problem

    Direct reinforcement learning can take time to converge for BS-switching controllers managing tens or hundreds of base stations.

    Source: §I · p. 3

  • Method

    TACT incorporates transfer learning into actor-critic, reusing learned strategies from historical periods or neighboring regions to speed learning on related tasks.

    Source: §I · pp. 4–5, §VI · p. 25

  • Results

    TACT outperforms classical actor-critic, and extensive simulations report effectiveness and robustness for the energy-saving framework.

    Source: §I · p. 5, §VI · p. 25

  • Takeaways & Limitations

    The proposed framework uses knowledge learned from historical periods to improve BS energy-saving strategies.

    Source: §VI · p. 25

    TACT’s convergence guarantee holds given certain restrictions that arise during learning.

    Source: §VI · p. 25

Abstract

from arXiv · show

Recent works have validated the possibility of improving energy efficiency in radio access networks (RANs), achieved by dynamically turning on/off some base stations (BSs). In this paper, we extend the research over BS switching operations, which should match up with traffic load variations. Instead of depending on the dynamic traffic loads which are still quite challenging to precisely forecast, we firstly formulate the traffic variations as a Markov decision process. Afterwards, in order to foresightedly minimize the energy consumption of RANs, we design a reinforcement learning framework based BS switching operation scheme. Furthermore, to avoid the underlying curse of dimensionality in reinforcement learning, a transfer actor-critic algorithm (TACT), which utilizes the transferred learning expertise in historical periods or neighboring regions, is proposed and provably converges. In the end, we evaluate our proposed scheme by extensive simulations under various practical configurations and show that the proposed TACT algorithm contributes to a performance jumpstart and demonstrates the feasibility of significant energy efficiency improvement at the expense of tolerable delay performance.

I. INTRODUCTION

The paper addresses energy-efficient BS switching without reliable traffic-load forecasts, while accounting for how switching choices affect future associations and energy use. It proposes TACT, which transfers learning across related periods or regions; the reported results indicate energy-saving feasibility and improved performance over classical actor-critic.

I. INTRODUCTION

  • BS switching choices change user associations and subsequent BS loads, so the paper frames energy minimization as a foresighted problem spanning current and future performance.Reliable traffic-load prediction remains challenging for practical applications.Source: §I · pp. 2–3
  • The paper models traffic variations as a Markov decision process and applies actor-critic reinforcement learning without requiring prior knowledge of BS traffic loads.The controller updates action probabilities using costs that primarily reflect energy consumption while also accounting for performance.Source: §I · p. 3
  • TACT incorporates transfer learning into actor-critic by reusing strategies learned in historical periods or neighboring regions to speed learning in related target tasks.The motivation is that direct reinforcement learning can take time to converge, particularly when a controller manages tens or hundreds of BSs.Source: §I · pp. 3–4
  • TACT outperforms classical actor-critic, while the learning framework saves energy without prior traffic-load knowledge and approaches the state-of-the-art scheme assumed to know loads fully.The authors identify the state-of-the-art scheme as.Source: §I · p. 5
  • The paper presents a convergence analysis for TACT, contributing to the reinforcement-learning literature, especially general actor-critic methods.The authors also report that TACT outperforms classical actor-critic in their comparison.Source: §I · p. 5

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model describes a centralized controller that selects BS active or sleeping modes and models fluctuating traffic with a finite-state Markov chain. The objective is to find feasible active BSs and user associations that minimize total cost without prior traffic-load knowledge.

A. System model

  • The model considers a region served by overlapping BSs and assumes a centralized controller selects each BS’s active or sleeping mode for the next stage.The modeled communication is downlink, from BSs to mobile terminals.Source: A. System model · p. 5
  • Traffic load density at a location is defined as λ(x)/µ(x), capturing variation associated with arrival rates and file sizes.The system partitions BS traffic loads into segments represented by finite-state indicators.Source: A. System model · pp. 5–6
  • A vector of per-BS finite-state indicators models regional traffic-load variation as a finite-state Markov chain.The vector state combines the individual BS state spaces.Source: A. System model · p. 6
  • For analytical convenience, transmission rates are time-averaged and held constant, excluding fast fading and dynamic inter-cell interference.Inter-cell interference is treated as static Gaussian-like noise.Source: A. System model · p. 7
  • An association indicator set is feasible when every BS load satisfies ρ_i < 1; sleeping BSs are assigned zero system load.For active BSs, system load is formed from the location-level load contributions.Source: A. System model · p. 7
  • The objective is to choose active BSs and a feasible user-association set that minimize total cost, with the learned switching strategy obtained without prior traffic-load knowledge.The framework is presented as the means for the controller to determine that strategy.Source: A. System model · p. 7

B. Problem formulation

The formulation chooses active base stations and user associations to minimize overall BS energy consumption while maintaining QoS. Its cost model accounts for both traffic-related energy and delay.

B. Problem formulation

  • BS energy includes a constant component and a remainder proportional to traffic load.The generalized model uses q_i for the constant power-consumption percentage and P_i for maximum power when BS i is fully utilized.Source: B. Problem formulation · p. 7
  • The cost also represents delay: for an M/G/s queue, the delay-optimal metric equals the number of flows, and Little’s law links minimizing it to average delay.The positive parameter ς, measured in W/s, expresses the equivalent cost of a waiting flow and the relative importance of delay.Source: B. Problem formulation · p. 8
  • The optimization selects active BSs and user associations to minimize energy consumption while ensuring QoS.The paper frames its overall objective as minimizing the BSs’ energy consumption in RANs.Source: B. Problem formulation · pp. 7–8

III. STOCHASTIC BS SWITCHING OPERATION IN REINFORCEMENT LEARNING FRAMEWORK

The paper models traffic variation and BS switching as an MDP. A policy maps traffic states to switching actions to minimize discounted cumulative cost.

III. STOCHASTIC BS SWITCHING OPERATION IN REINFORCEMENT LEARNING FRAMEWORK

  • As traffic emerges, the system transitions to a new state and returns the immediate cost to the switching controller.The cost is computed by the paper’s energy-cost function.Source: A. Markov decision process · pp. 8–9
  • At each stage, the traffic-load state informs a vector of BS switching actions; users then associate with remaining active BSs using an indicator based on metrics such as load or received signal strength.The state depends on traffic loads and the serving BSs.Source: A. Markov decision process · p. 8
  • A policy maps each state to an action to minimize discounted cumulative cost, with γ < 1 discounting future cost.The optimal policy satisfies the Bellman equation.Source: A. Markov decision process · p. 9

B. The actor-critic learning framework for energy saving

The framework uses reinforcement learning, specifically actor-critic, to learn BS switching without requiring prior traffic-load knowledge. It updates actions and value estimates as traffic and costs evolve.

B. The actor-critic learning framework for energy saving

  • Actor-critic reinforcement learning is used to solve the MDP without requiring prior knowledge of traffic loads.The actor selects actions, the environment returns a new state and cost, and the critic evaluates the action using a temporal-difference error.Source: B. The actor-critic learning framework… · p. 9
  • Stochastic action selection balances exploring alternative BS switching operations with exploiting past experience, using a Boltzmann distribution.The action-selection probabilities are updated after each stage.Source: B. The actor-critic learning framework… · p. 11
  • After switching, users associate with a BS according to the modified metric in, then transmit across slots as traffic loads change.The framework assumes the final action can meet traffic-load requirements, with an emergency response available to turn on BSs if needed.Source: B. The actor-critic learning framework… · p. 11
  • The critic compares the preceding value estimate with immediate cost plus discounted next-state value to compute the temporal-difference error.The resulting error feeds back to the actor for its policy update.Source: B. The actor-critic learning framework… · pp. 11–12
  • The actor uses the critic’s feedback to favor actions with lower foresighted cost, updating the selected action’s probability.The stated update increases an action’s selection probability when its foresighted cost is comparatively smaller.Source: B. The actor-critic learning framework… · p. 12
  • With infinite exploration—each action executed infinitely often in every state—the actor-critic value function and strategy converge with probability 1 to their optimal counterparts.The convergence claim is stated as the number of stages k tends to infinity.Source: B. The actor-critic learning framework… · p. 12

A. Motivation and formulation of transfer actor-critic algorithm

TACT transfers a learned policy to give a new task a potential performance jumpstart, while addressing the risk that source-task guidance may not fit the target. Its transfer influence fades as native learning proceeds.

A. Motivation and formulation of transfer actor-critic algorithm

  • The controller can use expertise from historical periods or neighboring regions and then swiftly reduce the influence of negative guidance.The policy encodes a tendency to select actions in particular states.Source: A. Motivation and formulation of… · pp. 12–14
  • Differences between source and target traffic can make a transferred policy guide switching in the wrong direction, despite similarities between tasks.The example contrasts higher source-period loads with lower target-period loads, where turning more BSs off may be appropriate.Source: A. Motivation and formulation of… · p. 13
  • TACT divides the overall policy into a native policy and an exotic policy carrying transferred knowledge.The method is introduced as a new policy-update approach to address misleading transfer guidance.Source: A. Motivation and formulation of… · p. 13
  • The transferred exotic policy can provide a performance jumpstart, while its transfer rate ζ(k) tends to zero as learning progresses.The native policy continues to update according to the classical actor-critic algorithm.Source: A. Motivation and formulation of… · pp. 13–14

B. Convergence analysis

The convergence analysis shows that TACT’s policy update tracks an ODE and that Algorithm 1 converges under the stated learning-rate and parameter conditions. Its proof establishes ODE tracking and a strict Lyapunov function for the tracked dynamics.

B. Convergence analysis

  • Boltzmann exploration with sufficiently large τ makes the executed-action count ν₂(s, a, k) grow without bound.The analysis also notes that this exploration is infinite while becoming greedy in the limit.Source: B. Convergence analysis · p. 15
  • The proposed policy update tracks an ODE when the transfer rate becomes negligible relative to the learning rate.The analysis states that p_o(s, a) asymptotically tracks the ODE solution under the transfer-rate condition.Source: B. Convergence analysis · p. 15
  • The proof interpolates updates into continuous time, establishes equicontinuity, and uses Arzelà–Ascoli to show limit sequences track the ODE.Only the value for the executed action is updated; the proof forms a sequence from those updated values before interpolation.Source: B. Convergence analysis · pp. 15–16
  • For sufficiently large p_t, V^π is a strict Lyapunov function, supporting convergence under the cited actor-critic theorem’s conditions.That theorem gives convergence with probability one and an arbitrarily small distance to π* as p_t tends to infinity.Source: B. Convergence analysis · pp. 16–17
  • With the required learning-rate and transfer-rate conditions and sufficiently large p_t and τ, Algorithm 1 converges regardless of initial p_n(s, a) and transferred p_e(s, a).The theorem’s conclusion applies regardless of the initial values of both the policy values and transferred knowledge.Source: B. Convergence analysis · p. 18

V. NUMERICAL ANALYSIS

The numerical analysis describes simulations in a 2 km × 2 km area containing five macro base stations and five micro base stations.

V. NUMERICAL ANALYSIS

  • The authors use extensive simulations under practical configurations to validate the energy-efficiency improvement of their scheme.The supplied passages describe the evaluation setup but do not report numerical outcomes.Source: §V · p. 18
  • The simulated area measures 2 km × 2 km.Source: §V · p. 18
  • The simulation scenario contains five macro base stations and five micro base stations.The paper refers to Fig. 4 for the deployment illustration.Source: §V · p. 18

USED SIMULATION PARAMETERS

The simulations examine energy saving and delay across traffic conditions and operating settings. They report that TACT benefits from transferred knowledge, while its performance depends on transfer and configuration choices.

USED SIMULATION PARAMETERS

  • At ς = 0, energy saving is greatest but delay increases slightly; higher ς reduces delay while making energy saving less pronounced.TACT's energy-delay tradeoff points are closer to the SOTA solutions across scenarios.Source: Figure 6 · p. 21, USED SIMULATION PARAMETERS · pp. 21–22
  • Lower homogeneous traffic arrival rates yield greater energy conservation, and CECR continues to fall as the controller learns which actions save energy.The learning schemes remain inferior to the SOTA scheme, especially at the start of simulations.Source: Figure 5 · p. 20, USED SIMULATION PARAMETERS · p. 21
  • TACT narrows the gap to the full-traffic-knowledge SOTA scheme when applied with learned knowledge, though learning schemes initially perform worse.The improvement is especially apparent early in simulation.Source: USED SIMULATION PARAMETERS · p. 21
  • A smaller Kullback-Leibler divergence between source and target tasks corresponds to a more efficient transfer effect.TACT also shows a relatively large performance improvement over classical AC, particularly at the beginning of simulation.Source: USED SIMULATION PARAMETERS · p. 22
  • Larger transfer-rate factor θ yields faster convergence and greater energy saving.Source: USED SIMULATION PARAMETERS · pp. 22–23, Figure 8 · p. 23
  • With periodically fluctuating traffic, TACT converges faster than classical AC.The simulation uses a sinusoidal traffic-arrival profile.Source: USED SIMULATION PARAMETERS · p. 23, Figure 9 · p. 24
  • Higher exploration temperature τ reduces energy savings, but TACT uses transferred knowledge to avoid undesirable actions and outperforms classical AC, especially at larger τ.Source: USED SIMULATION PARAMETERS · pp. 23–24
  • The reported performance trends also vary with file size and constant-power share, and the schemes are robust across the tested BS deployment scenarios.A larger constant-power share is associated with better performance; results also include a six-BS scenario.Source: USED SIMULATION PARAMETERS · p. 24

VI. CONCLUSION

The paper formulates BS switching under varying traffic as a Markov decision process and uses actor-critic learning with temporal transfer from historical periods. TACT is reported to converge under stated restrictions, and simulations show effectiveness and robustness across practical configurations.

VI. CONCLUSION

  • The paper develops a BS energy-saving framework that formulates switching under varying traffic loads as a Markov decision process and uses actor-critic learning to reduce energy consumption.Source: §VI · p. 24
  • TACT transfers learned knowledge from historical periods to exploit temporal traffic-load relevance and improve switching strategies.Source: §VI · p. 25
  • The algorithm is stated to provably converge under restrictions that arise during learning.Source: §VI · p. 25
  • Extensive simulations report effective and robust energy-saving schemes under various practical configurations.Source: §VI · p. 25
  • Spatial transfer is presented as potentially viable, but mapping knowledge is less straightforward when BS geographical deployments differ.The paper identifies spatial knowledge transfer as a more challenging issue for future work.Source: §VI · p. 25

APPENDIX

The appendix proof constructs shifted interpolated processes and relates their limits to an ordinary differential equation. It uses equicontinuity and subsequence convergence to establish the tracking argument.

APPENDIX

  • The proof indexes time intervals with K(t) and defines shifted processes from the interpolated policy sequence.Source: APPENDIX · pp. 26, 28, Figure 11 · p. 27
  • Because the shifted process is piecewise constant, the proof rewrites its relation using an integral and accounts for an interpolation error that tends to zero.Source: APPENDIX · p. 28
  • Equicontinuity yields a uniformly convergent subsequence on bounded time intervals, whose limit tracks the stated ODE for sufficiently large indices.Source: APPENDIX · p. 28
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