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A Reinforcement-Learning Approach to Proactive Caching in Wireless Networks

Samuel O. Somuyiwa, Andras Gyorgy, Deniz Gunduz

arXiv:1712.07084v1eess.SYcs.ITcs.NIcs.SYmath.IT

TL;DR

Dynamic content lifetimes, random user access, and changing channel conditions make it necessary to decide which contents to cache and when. The paper proves an optimal threshold structure and uses reinforcement learning to find tractable threshold approximations. Simulations show the schemes outperform reactive caching and perform close to lower bounds.

  • Problem

    Which relevant contents should be proactively cached, and when, given limited cache capacity, random user access, and energy costs that vary with channel conditions?

    Source: §I · p. 3

  • Method

    The paper proves a threshold-based optimal policy and uses reinforcement learning to optimize low-complexity LISO and LFA approximations.

    Source: §I · pp. 3–4

  • Results

    The proposed schemes significantly outperform reactive caching and approach the non-causal-access lower bound with small caches and the unlimited-capacity lower bound with larger caches.

    Source: §I · p. 4

  • Takeaways & Limitations

    LFA outperforms LISO, with a more significant performance gain when content-lifetime and channel processes have memory.

    Source: §I · p. 4

Abstract

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We consider a mobile user accessing contents in a dynamic environment, where new contents are generated over time (by the user's contacts), and remain relevant to the user for random lifetimes. The user, equipped with a finite-capacity cache memory, randomly accesses the system, and requests all the relevant contents at the time of access. The system incurs an energy cost associated with the number of contents downloaded and the channel quality at that time. Assuming causal knowledge of the channel quality, the content profile, and the user-access behavior, we model the proactive caching problem as a Markov decision process with the goal of minimizing the long-term average energy cost. We first prove the optimality of a threshold-based proactive caching scheme, which dynamically caches or removes appropriate contents from the memory, prior to being requested by the user, depending on the channel state. The optimal threshold values depend on the system state, and hence, are computationally intractable. Therefore, we propose parametric representations for the threshold values, and use reinforcement-learning algorithms to find near-optimal parametrizations. We demonstrate through simulations that the proposed schemes significantly outperform classical reactive downloading, and perform very close to a genie-aided lower bound.

I. INTRODUCTION

The paper formulates proactive caching for dynamic content and wireless channels as an average-cost decision problem, then develops threshold policies and tractable approximations. Simulations show the learned schemes outperform reactive caching and approach lower bounds, with LFA outperforming LISO.

II. SYSTEM MODEL

  • The model uses slotted time, random content arrivals and lifetimes, stochastic channel quality and user access, and a finite-capacity cache.Source: §I · p. 3, §II · pp. 4, 6

I. INTRODUCTION

  • The optimal policy uses channel-dependent thresholds to cache or remove contents according to their remaining lifetimes, but state-dependent thresholds are impractical to compute and store.Source: §I · pp. 3–4
  • LISO assigns a threshold per pair of cache-boundary lifetimes, while LFA models thresholds for each lifetime pair as a linear function of system state.Source: §I · p. 4
  • The proposed schemes significantly outperform reactive caching, approaching the non-causal-access lower bound with small caches and the unlimited-capacity lower bound with larger caches.Source: §I · p. 4
  • LFA outperforms LISO, and policy gradient with the likelihood-ratio method finds a better solution than with finite differences.Source: §I · p. 4

1) User Access Model:

User accesses are modeled as an arrival process with i.i.d. inter-arrival times, under either bounded or geometric timing assumptions.

1) User Access Model:

2) Content Generation Model:

The system model specifies stochastic content generation and channel costs, while the optimal-solution section frames cache management as an average-cost MDP and describes conditions for an optimal deterministic policy.

2) Content Generation Model:

3) Channel Model:

  • Download cost is positive, i.i.d. across time, and bounded; the model also assumes zero download delay and independent system sequences.Source: 3) Channel Model · pp. 6–7

III. OPTIMAL SOLUTION

  • The paper derives a general optimal-policy structure for MDPs with side information and applies it to cache management.Source: §III · p. 7

A. Standard MDP model

  • A standard MDP is defined by state and action spaces, transition probabilities, and costs; under the stated chain conditions, a deterministic policy minimizes infinite-horizon average cost.Source: A. Standard MDP model · pp. 7–8

B. MDPs with side information (MDP-SI)

The paper treats channel cost as i.i.d. side information available before each decision, then uses the resulting MDP-SI formulation to establish piecewise-constant optimal decisions under stated conditions.

B. MDPs with side information (MDP-SI)

C. Structure of the optimal policy in MDP-SI

D. Structure of the optimal cache management policy

The optimal cache policy orders candidate exchanges by remaining lifetime and uses channel-cost thresholds to decide how many to perform; finite-capacity thresholds depend on the system state.

D. Structure of the optimal cache management policy

IV. LOW-COMPLEXITY CACHING SCHEMES VIA POLICY APPROXIMATION

The optimal threshold policy varies across system states, making exact computation infeasible for reasonable cache sizes. The paper therefore approximates the policy space with simpler parameterizations that can be optimized from observations.

IV. LOW-COMPLEXITY CACHING SCHEMES VIA POLICY APPROXIMATION

  • State-dependent thresholds across many system states and simple actions make the optimal policy infeasible to compute for reasonable cache sizes.Thresholds depend on content lifetimes inside and outside the cache and time since the last user access.Source: §IV · p. 15
  • Policy approximation addresses this complexity by representing the policy space with simpler parameterized forms.The goal is to avoid computing the prohibitively large set of state-specific thresholds.Source: §IV · p. 15
  • Under the IRM access model, two low-dimensional approximations enable feasible policy search, with parameters optimized from observations rather than known system statistics.The observations may come from the real system or simulations using a generative model, supporting reinforcement learning in unknown environments.Source: §IV · pp. 15–16

A. The longest lifetime in–shortest lifetime out (LISO) policy

The paper presents LISO, a state-independent threshold policy, and extends it with LFA, which uses cache-lifetime composition when setting thresholds.

A. The longest lifetime in–shortest lifetime out (LISO) policy

  • LISO assigns each simple action a state-independent threshold for swapping the shortest-lived cached content with the longest-lived uncached content when channel cost is below that threshold.It is a suboptimal threshold-based policy.Source: A. The longest lifetime in–shortest… · p. 16
  • LISO's search space can be narrowed by forbidding swaps that replace a cached content with a shorter-lived one and using the policy's monotonic threshold structure.The monotonicity relations constrain thresholds across pairs of cached and uncached lifetimes.Source: A. The longest lifetime in–shortest… · p. 16

B. Linear function approximation (LFA) policy

  • LFA extends LISO by using features that describe the cache's remaining-lifetime composition when determining action thresholds.The features are based on the number of cached contents at each remaining lifetime; this information can help estimate whether a downloaded content will be removed before expiry or consumption.Source: B. Linear function approximation (LFA)… · pp. 16–17
  • LISO is a special case of LFA in which each action's threshold parameters are identical across cache-state features.The LFA policy space is parameterized by action and cache-state feature.Source: B. Linear function approximation (LFA)… · p. 17

V. POLICY SEARCH METHODS

Policy-gradient methods optimize the parameterized caching policies by minimizing expected average cost using trajectory-based estimates. The finite-difference method estimates gradients by perturbing policy parameters between trajectories.

V. POLICY SEARCH METHODS

  • Policy-gradient methods use model-free gradient descent over policy parameters to minimize the expected average cost of the resulting policy.The parameter updates use gradient estimates obtained from independent finite trajectories and Monte Carlo rollouts.Source: §V · pp. 17–18
  • Policy evaluation estimates average cost from a sample trajectory, while exploration generates new trajectories by perturbing actions or policy parameters.The parameter perturbations in FDM are drawn coordinate-wise from a uniform range around the current values.Source: §V · p. 18, A. Finite difference method (FDM) · p. 18

A. Finite difference method (FDM)

  • Finite-difference method estimates the gradient by comparing trajectory costs under the current parameter vector and perturbed parameter vectors.Perturbations are applied to the parameter vector at the beginning of each trajectory; the gradient estimate is obtained by linear regression over independent trajectories.Source: A. Finite difference method (FDM) · p. 18

B. Likelihood-ratio method (LRM)

The likelihood-ratio method uses randomized action probabilities and trajectory samples to estimate policy gradients. A baseline reduces estimate variance without introducing bias.

B. Likelihood-ratio method (LRM)

  • LRM randomizes each simple action's selection probability using a sigmoid policy, then attempts actions in order until the first failure.The ordered actions pair cached contents from shortest to longest remaining lifetime with uncached contents from longest to shortest.Source: B. Likelihood-ratio method (LRM) · p. 19
  • The likelihood-ratio gradient estimate is averaged over independent policy trajectories, and its expectation can be approximated by sample averages without knowing the trajectory density.The trajectory likelihood is used in the gradient expression, while the policy's parametric form supplies quantities computed from the sampled trajectory.Source: B. Likelihood-ratio method (LRM) · pp. 19–20
  • A baseline vector reduces variance in the gradient estimate without adding bias.The baseline is selected to minimize the variance of each gradient-coordinate estimate.Source: B. Likelihood-ratio method (LRM) · p. 20
  • Lower bounds are used to evaluate the performance loss introduced by the low-complexity caching policies.The paper next presents those bounds after describing the policy-gradient methods.Source: B. Likelihood-ratio method (LRM) · p. 20

VI. LOWER BOUNDS

The paper derives two average-cost lower bounds by relaxing system constraints: unlimited cache capacity and non-causal knowledge of user access times. Each relaxed problem has a threshold-based optimal policy whose performance can be estimated with Monte Carlo rollouts.

VI. LOWER BOUNDS

  • Both lower bounds relax system constraints and estimate optimal-policy performance by averaging costs over Monte Carlo trajectories.The unlimited-cache bound and the non-causal-access-time bound become tight under different settings.Source: §VI · p. 20

A. Lower bound with unlimited cache capacity (LB-UC)

  • With unlimited cache capacity, contents can be downloaded independently, without removing or replacing cached contents.This is the LB-UC relaxation; its threshold structure follows from the earlier optimal-policy result.Source: A. Lower bound with unlimited cache… · pp. 20–21

B. Lower bound with non-causal knowledge of the user access times (LB-NCK)

  • With non-causal access-time knowledge, contents that expire before the next access are never downloaded, and the optimal download decision has a threshold structure.The finite-horizon problem depends on time until the next access and current channel cost.Source: B. Lower bound with non-causal… · p. 21

T NCK

The simulations model random content arrivals and lifetimes, random user access, and time-varying wireless conditions. They compare caching policies with reactive and random baselines and evaluate them under a specified channel model and algorithm setup.

VII. NUMERICAL RESULTS

  • The evaluation compares FDM and LRM implementations with lower bounds, reactive downloading, and random caching.Performance tests use 100 trajectories of 5000 slots; algorithm updates use 300-slot trajectories, with 100 trajectories per FDM update and 20 per LRM update.Source: §VII · p. 22, A. System Setup · p. 23

A. System Setup

  • Contents arrive in random numbers with random lifetimes, while the user accesses the system independently with probability pa = 0.25 per slot.The simulation draws the number of generated contents uniformly from 1 to Mmax and lifetimes from 5, 10, …, Kmax.Source: A. System Setup · p. 22
  • The channel model uses Shannon capacity with an LTE-consistent urban-micro pathloss model and time-varying user distance.The user distance is drawn uniformly from 50 to 250 m; the model assumes a single serving base station.Source: A. System Setup · pp. 22–23
  • The Fig. 2 setup plots average energy cost against cache capacity with Kmax = 15, Mmax = 8, and pa = 0.25.The caption specifies these conditions but does not give plotted values.Source: Figure 2 · p. 24

B. Performance Evaluation

In the baseline evaluation, proactive caching substantially reduces energy cost relative to reactive delivery, with LISO approaching the unlimited-cache bound at larger capacities. LFA and LRM improve performance in low-capacity settings; under memory in content lifetimes and user location, LFA’s advantage over LISO is larger than in the i.i.d. case.

B. Performance Evaluation

  • At B = 30, LISO reduces energy consumption by approximately 60% over reactive delivery, and at B ≥ 40 it nearly meets LB-UC.The paper attributes the larger-capacity result to enough room to store contents that remain relevant until access, with few removals needed.Source: B. Performance Evaluation · pp. 24–25
  • In low-capacity settings, LFA with FDM gains up to 4.4% over LISO with FDM, while LFA with LRM gains up to 5.6% over LISO with FDM.LRM improves LISO by up to 4.2% over FDM; below B = 10, all compared policies closely follow LB-NCK.Source: B. Performance Evaluation · p. 25
  • As Kmax increases, average energy cost rises, and LISO with LRM gains more over LISO with FDM.The figure plots average energy cost against maximum content lifetime for cache capacities B = 20 and 30.Source: B. Performance Evaluation · p. 25, Figure 3 · p. 26
  • LRM initially performs worse than FDM, begins converging faster after about 250 trajectories, and reaches optimal performance after approximately 1000.The convergence comparison is plotted against number of rollouts.Source: B. Performance Evaluation · p. 26, Figure 4 · p. 26

C. Stochastic Process with Memory

  • With memory in content lifetimes and user location, LFA’s gain over LISO is approximately 2%, versus approximately 0.75% in the i.i.d. case.The paper links the larger gain to existing contents providing information about future states and LFA accounting for all remaining lifetimes.Source: C. Stochastic Process with Memory · pp. 27–28

VIII. CONCLUSIONS

  • The conclusion reports that both low-complexity schemes perform close to optimal in simulations, with LFA generally better than LISO.The paper identifies nonlinear cost functions and multi-user scenarios as future extensions.Source: §VIII · pp. 28–29

APPENDIX A

The appendix establishes the structural result by replacing non-unique policy representations with equivalence classes, then minimizing over side information to obtain a piecewise-constant policy.

APPENDIX A

  • The proof groups policies that agree almost surely on side information into equivalence classes to address non-unique representations.It selects one representative from each class.Source: Appendix A · p. 29
  • The representative-policy set is compact under the metric given by the probability that two policies differ, and the resulting MDP is equivalent to the original almost surely.This supports transferring the structural result back to the original problem.Source: Appendix A · p. 29
  • Minimizing independently for each side-information value yields a piecewise-constant policy over an interval partition.The proof then converts that policy back to the original MDP with side information.Source: Appendix A · pp. 29–30
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