Source-linked AI summary
Competitive caching with machine learned advice
Thodoris Lykouris, Sergei Vassilvitskii
TL;DR
The paper studies how to combine machine-learned predictions with online algorithms that must remain robust to uncertainty and prediction errors. It introduces a black-box framework and applies it to caching by modifying Marker, obtaining error-dependent competitive ratios capped by O(log k), with favorable empirical results from simple predictors.
Problem
Online algorithms provide worst-case robustness but may be overly cautious, while machine-learned predictions can fail on outliers or distribution shifts and need robust use.
Method
The paper introduces a black-box framework for augmenting online algorithms with machine-learned advice and instantiates it by adapting Marker for caching.
Results
2 + O(min(η/Opt, log k)) is the caching competitive ratio, improving with lower prediction error and degrading gracefully toward the worst-case bound.
Takeaways & Limitations
Predictive Marker combines prediction-sensitive improvements with worst-case protection, and empirically outperforms LRU, Marker, and direct predictor use on public data.
Takeaways & Limitations
The framework does not address where predictors come from or how learnable they are, leaving model and loss-function trade-offs open.
Abstract
from arXiv · showhide
Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution as compared to an offline optimum. On the other hand, machine learning algorithms are in the business of extrapolating patterns found in the data to predict the future, and usually come with strong guarantees on the expected generalization error. In this work we develop a framework for augmenting online algorithms with a machine learned oracle to achieve competitive ratios that provably improve upon unconditional worst case lower bounds when the oracle has low error. Our approach treats the oracle as a complete black box, and is not dependent on its inner workings, or the exact distribution of its errors. We apply this framework to the traditional caching problem -- creating an eviction strategy for a cache of size $k$. We demonstrate that naively following the oracle's recommendations may lead to very poor performance, even when the average error is quite low. Instead we show how to modify the Marker algorithm to take into account the oracle's predictions, and prove that this combined approach achieves a competitive ratio that both (i) decreases as the oracle's error decreases, and (ii) is always capped by $O(\log k)$, which can be achieved without any oracle input. We complement our results with an empirical evaluation of our algorithm on real world datasets, and show that it performs well empirically even using simple off-the-shelf predictions.
1 Introduction
The paper asks how machine-learned predictions can improve online decisions without sacrificing worst-case robustness, focusing on caching. It develops Predictive Marker, whose guarantees improve with prediction accuracy while remaining bounded by classical online performance.
- Online algorithms hedge against unknown futures but can incur high competitive ratios because their guarantees target worst-case inputs.Machine learning predicts future events, motivating a combination of predictive power and online robustness.
- Caching motivation: Caching requires eviction decisions for a size-k cache, with deterministic algorithms incurring competitive ratio Ω(k) and randomized algorithms Θ(log k).The caching objective is to minimize cache misses while serving sequential requests.
- Main result: 2 + O(min(η/Opt, log k)) is the competitive ratio achieved using a predictor with total error η.The ratio improves when η is small and degrades gracefully toward the worst-case bound when η is large.
- Our contribution: Predictive Marker adapts the Marker algorithm to incorporate predictions while retaining worst-case competitiveness.Its design aims to improve as oracle error decreases and remain comparable to the best online algorithm when predictions are unreliable.
- Main result: Naively following predicted eviction recommendations can perform poorly even when average prediction error is small.The paper motivates algorithmic safeguards rather than blind reliance on the predictor.
- Empirical evaluation: Empirically, Predictive Marker outperforms LRU, the original Marker algorithm, and direct predictor use on public data with off-the-shelf models.The paper also uses faster binary search as an illustrative example of prediction-dependent algorithmic cost.
2 Online Algorithms with Machine Learned Advice
The OMLA framework formalizes how online algorithms can use machine-learned advice by representing feature-augmented requests, predictions, and losses. It evaluates algorithms through prediction-dependent competitive guarantees while highlighting trade-offs in model and loss-function choice.
- OMLA framework: OMLA combines online algorithms with machine-learned predictions and evaluates performance as a function of predictor error.The framework is introduced for general problems before being instantiated for caching.
- Problem representation: Feature-augmented items pair each request’s underlying element with features that can support meaningful predictions.For caching, features may include request history and temporal patterns.
- Prediction model: A predictor maps item features to labels in a chosen prediction model, with deterministic mappings covered directly and randomized mappings handled through Jensen’s inequality.The label space represents information needed to solve the task approximately optimally.
- Loss and error: Loss functions quantify prediction error, and absolute or squared loss for caching can decompose error across requested items.Selecting the loss function creates a trade-off between predictor learnability and resulting performance guarantees.
- Desiderata: The framework seeks algorithms that are consistent with accurate predictors, robust to inaccurate ones, and competitive in the worst case.Exact 1-consistency may be infeasible because of computational difficulty or tension with robustness, so a small constant β is allowed.
- Scope and limitations: Choosing the prediction model and loss function requires balancing learnability against accuracy, a question the framework leaves as an open direction.The framework can also extend beyond competitive analysis to metrics such as space complexity.
3 Main result: Predictive Marker
Predictive Marker combines machine-learned predictions with Marker-style randomized eviction to improve caching performance when predictions are accurate while preserving worst-case protection. Blindly following predictions can be inefficient even with low average error, whereas Predictive Marker achieves an error-sensitive competitive ratio capped by a logarithmic function of cache size.
- Motivation: Blindly evicting the element predicted furthest in the future can perform poorly in both robustness and competitiveness, even when prediction error is small.The paper motivates algorithmic safeguards rather than direct reliance on the predictor.
- Predictive Marker: Predictive Marker adapts the Marker algorithm to incorporate predictions while retaining worst-case guarantees.The approach combines prediction-guided decisions with randomized marking and eviction behavior.
- Main result: 2 · min(1 + 5ϵ, 2H_k) is the competitive ratio of the ϵ-assisted Predictive Marker algorithm, where H_k is the k-th Harmonic number.H_k = 1 + 1/2 + ··· + 1/k, so the bound is capped by a logarithmic term in k.
- Main result: The competitive-ratio theorem applies to any loss function whose spread S_ℓ is concave in cumulative prediction error.Corollaries specialize the guarantee to absolute and squared loss metrics.
- Analysis: The analysis bounds each chain’s expected length by min(1 + 2S_ℓ(η_r,c), 2 log k), linking prediction error to stale-element misses.If the chain switches to random evictions, its expected length is capped by 2H_k; otherwise, stale-element misses are controlled by the loss spread.
- Tightness: The analysis is tight for marking algorithms that use the predictor deterministically, so robustness cannot be improved within that class.This establishes a boundary on deterministic prediction use in marking-based caching algorithms.
4 Discussion and extensions
The discussion develops robustness properties, practical extensions, and a black-box reduction for combining predictive and worst-case online algorithms. Predictive Marker adapts to localized prediction quality, robustifies LRU, and generalizes beyond caching.
- Trade-offs: An adjustable switching point trades competitiveness against robustness by controlling when Predictive Marker abandons predictions for random evictions.Earlier switching is more conservative; later switching trusts the predictor more but worsens guarantees when predictions are unreliable.
- Locality: Localized prediction errors do not propagate across phases because the phase-based analysis resets, preserving an O(Hk) bound in every phase.Bad phases receive the logarithmic worst-case guarantee, while other phases can benefit from predictive advice.
- Robustifying LRU: Predictive Marker expresses LRU’s recency rule as a predictor, retaining most of its predictive power while guaranteeing a logarithmic worst-case bound.Without switching to random evictions, the LRU-assisted Predictive Marker is exactly LRU.
- Black-box combination: The black-box reduction extends beyond caching when the cost of reconciling the robust and worst-case algorithm states can be bounded, including the k-server problem.
- Black-box combination: A black-box construction combines an α-robust algorithm with a γ-competitive algorithm into one algorithm that is 9α-robust and 9γ-competitive.The construction simulates both algorithms in parallel and switches between their strategies while reconciling cache states.
5 Experiments
Experiments evaluate Predictive Marker on public datasets with synthetic and off-the-shelf predictions against standard baselines. Across these settings, it performs best or consistently better, while blind oracle use is fragile under error.
- Datasets: The evaluation uses BrightKite check-in sequences and CitiBike trip histories from New York City.The datasets represent different domains and provide caching instances from public data.
- Setup: Experiments measure competitive ratio, defined as misses incurred by a strategy divided by the optimum number of misses.
- Algorithms: The comparison includes LRU, Marker, Predictive Marker, and Blind Oracle, with Predictive Marker configured to avoid switching to random evictions.
- Synthetic predictions: Predictive Marker consistently outperforms LRU and standard Marker on synthetic predictions and degrades slowly as average error increases.Figure 1 varies oracle error with k = 10 on the BK dataset.
- Synthetic predictions: Blind Oracle performs well only at very low error and quickly becomes costly as oracle error increases.
- PLECO predictions: 2.5% better than the next-best method, LRU, Predictive Marker’s PLECO results are statistically significant at p < 0.001.The ranking is not sensitive to cache size, and the off-the-shelf PLECO model was not tuned for next-appearance prediction.
- PLECO predictions: Using the predictor with Marker yields a large performance advantage over using the same predictor directly as Blind Oracle.The result supports the paper’s claim that algorithmic handling of predictions matters empirically.
6 Conclusion
The paper combines online algorithms with machine learned predictors for caching, tying competitive performance to oracle accuracy. Its approach aims to use prediction safely while retaining worst-case guarantees and improving empirically over LRU.
- The framework augments online algorithms with machine learned predictors while preserving rigorous performance guarantees.
- For classical caching, the oracle-based algorithm achieves a competitive ratio directly tied to the oracle’s accuracy.
- The caching algorithm avoids problems caused by rare wildly inaccurate predictions and empirically improves over LRU even with simple predictors.
A Proof of Lemma 3.1
The proof characterizes sequence pairs minimizing absolute or squared loss under spread constraints, then derives upper bounds for each loss using odd-length sequences.
- The auxiliary lemma reduces loss minimization to pairs with constant B_T and consecutive elements in A_T.For odd T = 2n + 1, the minimizing pair is A_T = (0, . . . , 2n) and B_T = (n, . . . , n).
- The proof restricts attention to odd T = 2n + 1 and T ≥3 to obtain an upper bound on spread that is tight up to small constant factors.
- T = √4m + 1 yields absolute loss at least m, producing an upper bound on absolute-loss spread.
- 3√14m bounds the spread under squared loss.