Source-linked AI summary
Improving Online Algorithms via ML Predictions
Ravi Kumar, Manish Purohit, Zoya Svitkina
TL;DR
The paper asks how online algorithms can use machine-learned predictions when future inputs are uncertain. It develops prediction-augmented algorithms for ski rental and non-clairvoyant job scheduling, with guarantees that improve under accurate predictions while retaining worst-case protection. The paper also reports practical experiments and identifies extending the approach to other online problems and using prediction-error distributions as future directions.
Problem
Online algorithms must make decisions without knowing future durations or arrivals, motivating methods that use predictions while retaining performance guarantees.
Method
The paper modifies classical online algorithms for ski rental and non-clairvoyant job scheduling to use machine-learned predictions through a robustness-consistency framework.
Results
The algorithms are robust to prediction error and consistent with perfect predictions, including (1 + 1/λ)-robust and (1 + λ)-consistent guarantees for deterministic ski rental and (2/(1 − λ))-robust and (1/λ)-consistent guarantees for randomized scheduling.
Takeaways & Limitations
Prediction-augmented online algorithms can achieve guarantees beyond classical lower bounds while preserving worst-case constant competitiveness.
Takeaways & Limitations
The paper leaves using the machine-learning predictor’s error distribution to further improve the bounds as future work.
Abstract
from arXiv · showhide
In this work we study the problem of using machine-learned predictions to improve the performance of online algorithms. We consider two classical problems, ski rental and non-clairvoyant job scheduling, and obtain new online algorithms that use predictions to make their decisions. These algorithms are oblivious to the performance of the predictor, improve with better predictions, but do not degrade much if the predictions are poor.
1 Introduction
The paper studies how machine-learned predictions can improve online algorithms under uncertainty, using ski rental and non-clairvoyant job scheduling. It develops algorithms that balance performance with prediction quality through robustness and consistency guarantees.
- Motivation: Machine-learned predictions are used to improve online decisions when future inputs, such as skiing duration or job runtimes, are unknown.The paper motivates prediction-augmented algorithms as a way to address uncertainty in online computational tasks.
- Problems: The paper studies ski rental and non-clairvoyant job scheduling, representing rent-or-buy decisions and scheduling without known processing times.In ski rental, the unknown quantity is the number of skiing days; in scheduling, the scheduler learns a job’s runtime only when it finishes.
- Framework: Algorithms are evaluated by competitive-ratio functions c(η), with robustness bounding performance for all prediction errors and consistency measuring performance under perfect predictions.Robustness captures worst-case behavior, while consistency captures the zero-error case.
- Results: For ski rental, the deterministic algorithm is (1 + 1/λ)-robust and (1 + λ)-consistent, while a randomized algorithm improves these bounds.Here λ ∈ (0, 1) is a tunable hyperparameter; the randomized bounds are stated in the paper’s result passage but truncated in the supplied text.
- Results: For non-clairvoyant scheduling, the randomized algorithm is (2/(1 − λ))-robust and (1/λ)-consistent.These consistency guarantees can circumvent classical lower bounds because the algorithms use predictions.
- Algorithm design: Naively using predictions can destroy robustness, so the proposed algorithms incorporate predictions judiciously into classical online algorithms and are tested empirically.The paper reports experiments indicating that the algorithms are practical and perform well compared with methods that do not use predictions.
2 Ski rental with prediction
The ski-rental algorithms use predictions of skiing duration to balance consistency under accurate predictions against robustness under errors. Deterministic and randomized designs provide explicit trade-offs, with randomization improving the ski-rental trade-off and extending to varying demand.
- 2.1 Warmup: A simple consistent, non-robust algorithm: The simple prediction-based algorithm is 1-consistent but can have an unbounded competitive ratio when predictions are poor.It buys immediately when the predicted duration reaches the buying threshold and otherwise keeps renting.
- 2.2 A deterministic robust and consistent algorithm: With λ ∈(0, 1), the deterministic algorithm is (1 + 1/λ)-robust and (1 + λ)-consistent.Varying λ creates a smooth trade-off between robustness and consistency.
- 2.2 A deterministic robust and consistent algorithm: The deterministic algorithm becomes more prediction-sensitive as λ approaches zero and more conservative as λ approaches one.Small λ favors better competitive ratios when prediction error is small, whereas large λ yields greater robustness.
- 2.3 A randomized robust and consistent algorithm: The randomized algorithm is (1 + 1/b)/(1 − e^−(λ−1/b))-robust and λ/(1 − e^−λ)-consistent.It samples the purchase day from prediction-dependent probability distributions.
- 2.4 Extensions: The randomized algorithm guarantees smaller consistency for a given robustness guarantee than the deterministic algorithm, and both extend to varying demand.For varying demand, the prediction error is total L1 error, and the same robustness and consistency guarantees apply.
3 Non-clairvoyant job scheduling with prediction
The paper studies non-clairvoyant scheduling with predicted job lengths, combining prediction-driven ordering with round-robin execution to obtain consistency and robustness guarantees.
- The scheduler minimizes total completion time when job processing times are unknown until completion, while allowing preemption and resumption.
- Algorithms: SPJF executes jobs in increasing predicted-length order and is optimal with perfect predictions, but its worst-case performance is unbounded under bad predictions.
- Algorithms: Preferential round-robin combines SPJF and round-robin by running them concurrently at rates controlled by λ.
- Algorithms: The combined algorithm has competitive ratio at most min{α/λ, β/(1−λ)} when combining monotonic algorithms with ratios α and β.
- Guarantees: The preferential round-robin algorithm is 2/(1−λ)-robust and 1/λ-consistent.
- Guarantees: When λ > 0.5, sufficiently accurate predictions let preferential round-robin beat round-robin’s competitive ratio of 2.
4 Experimental results
Experiments evaluate prediction-aware algorithms for ski rental and non-clairvoyant scheduling under simulated prediction errors. In scheduling, preferential round-robin maintains round-robin-level performance as prediction errors become large, unlike SPJF.
- Ski rental: Ski-rental experiments use buying cost b = 100, actual durations uniformly sampled from [1, 4b], and normally distributed prediction errors.
- Non-clairvoyant scheduling: Scheduling experiments generate 50 jobs with processing times sampled independently from a Pareto distribution with exponent α = 1.1.
- Non-clairvoyant scheduling: Figure 2b compares the three scheduling algorithms’ average competitive ratios over 1000 trials at varying prediction-error standard deviations.
- Non-clairvoyant scheduling: SPJF performs very well at low prediction error but quickly deteriorates as prediction errors increase.
- Non-clairvoyant scheduling: With λ = 0.5, preferential round-robin performs no worse than round-robin even when prediction errors are very large.
5 Conclusions
The paper extends the study of machine-learned predictions for improving worst-case online-algorithm performance. It identifies broader applications and using prediction-error distributions as future directions.
- The paper advances the use of ML predictions to provably improve the worst-case performance of online algorithms.
- Potential extensions include applying predictions to other online problems such as k-server and portfolio optimization.
- Using the ML predictor’s error distribution to further improve the bounds is proposed as another research direction.
A Deferred Proofs
The deferred proofs establish auxiliary exponential inequalities and prove non-negativity of a constrained quadratic, supporting the stated analytical bounds. They also derive a lemma under λ ∈(1/b, 1).
- For x ∈(0, 1], exponential comparison gives ex ≤e1/x, while for y ≤1, ey ≤1/(1−y).
- A function h is shown concave for x ≥0 by bounding its second derivative with ex ≥1 + x + x^2/2.
- Lemma A.2 assumes integer b ≥2 and λ ∈(1/b, 1), then establishes the stated exponential inequality after setting y = 1/b.
- The proof rewrites inequality (3) as the quadratic f(y) and minimizes it over 0 ≤y ≤λ.
- Under y ≥0, the minimum is attained at y = 0; substitution completes the non-negativity argument and the proof.