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Shift-Table: a Low-Latency Learned Index for Range Queries Using Model Correction

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Shift-Table: a Low-Latency Learned Index for Range Queries Using Model Correction Shift-Table: A Low-latency Learned Index for Range Queries using Model Correction Ali Hadian Thomas Heinis Imperial College London Imperial College London ABSTRACT retrieve the entire result set. Therefore, processing a range query Indexing large-scale databases in main memory is still challeng- 퐴 < key < 퐵 is equivalent to finding the first result, i.e., the ing today. Learned index structures — in which the core com- smallest key in the dataset that is greater than or equal to 퐴 (sim- ponents of classical indexes are replaced with machine learning ilar to lower_bound(A) in the C++ Library standard). A learned models — have recently been suggested to significantly improve index can be built by fitting a regression model to the cumulative performance for read-only range queries. distribution function (CDF) of the key distribution. The learned However, a recent benchmark study shows that learned in- CDF model can be used to determine the physical location where dexes only achieve limited performance improvements for real- the lower-bound of the query resides, i.e., pos¹Aº = # × 퐹\ ¹Aº world data on modern hardware. More specifically, a learned where N is the number of keys and 퐹\ is the learned CDF model model cannot learn the micro-level details and fluctuations of with model parameters \. data distributions thus resulting in poor accuracy; or it can fit to Learned indexes are very efficient for sequence-like data (e.g., the data distribution at the cost of training a big model whose machine-generated IDs), as well as synthetic data sampled from parameters cannot fit into cache. As a consequence, querying a statistical distributions. However, a recent study using the Search- learned index on real-world data takes a substantial number of On-Sorted-Data benchmark (SOSD) [21] shows that for real- memory lookups, thereby degrading performance. world data distributions, a learned index has the same or even In this paper, we adopt a different approach for modeling a poorer performance compared to algorithmic indexes. For many data distribution that complements the model fitting approach real-world data distributions, the CDF is too complex to be learned of learned indexes. We propose Shift-Table, an algorithmic layer efficiently by a small cache-resident model. The data distribution that captures the micro-level data distribution and resolves the of real-world data has "too much information" to be accurately local biases of a learned model at the cost of at most one memory represented by a small machine-learning model, while an accu- lookup. Our suggested model combines the low latency of lookup rate model is needed for an accurate prediction. One can of course tables with learned indexes and enables low-latency processing of use smaller models that fit in memory with the cost of lower pre- range queries. Using Shift-Table, we achieve a speedup of 1.5X to diction accuracy, but will end up in searching a larger set of 2X on real-world datasets compared to trained and tuned learned records to find the actual result which consequently increases indexes. memory lookups and degrades performance. Alternatively, a high accuracy can be achieved by training a bigger model, but accessing the model parameters incurs multiple cache misses 1 INTRODUCTION and also increases memory lookups, reducing the margins for Trends in new hardware play a significant role in the way we performance improvement. design high-performance systems. A recent technological trend is In this paper, we address the challenge of using learned models the divergence of CPU and memory latencies, which encourages on real-world data and illustrate how the micro-level details decreasing random memory access at the cost of doing more (e.g., local variance) of a cumulative distribution can dramatically compute on cache-resident data [24, 40, 43]. affect the performance of a range index. We also argue thata A particularly interesting family of methods exploiting the pure machine learning approach cannot shoulder the burden of memory/CPU latency gap are learned index structures. A learned learning the fine-grained details of an empirical data distribution index uses machine learning instead of algorithmic data struc- and demonstrate that not much improvement can be achieved tures to learn the patterns in data distribution and exploits the by tuning the complexity or size thresholds of the models. trained model to carry out the operations supported by an al- We suggest that by going beyond mere machine learning mod- gorithmic index, e.g., determining the location of records on els, the performance of a learned index architecture can be sig- physical storage [7, 12, 17, 23, 24, 28]. If the learned index man- nificantly improved using a complementary enhancement layer arXiv:2101.10457v1 [cs.DB] 25 Jan 2021 ages to build a model that is compact enough to fit in processor rather than over-emphasizing on the machine learning tasks. Our cache, then the results can ideally be fetched with a single access suggested layer, called Shift-Table is an algorithmic solution that to main memory, hence outperforming algorithmic structures improves the precision of a learned model and effectively acceler- such as B-trees and hash tables. ates the search performance. Shift-Table, targets the micro-level In particular, learned index models have shown a great poten- bias of the model and significantly improves the accuracy, at the tial for range queries, e.g., retrieving all records where the key is cost of only one memory lookup. The suggested layer is optional in a certain range 퐴 < key < 퐵. To enable efficient retrieval of and applied after the prediction; it can hence be switched on or range queries, range indexes keep the records physically sorted. off without re-training the model. Therefore, retrieving the range query is equivalent to finding Our contributions can be summarized as follows: the first result and then sequentially scanning the records to © 2021 Copyright held by the owner/author(s). Published in Proceedings of the • We identify the problem of learning a range index for real- 24th International Conference on Extending Database Technology (EDBT), March world data, and illustrate the difficulty of learning from 23-26, 2021, ISBN 978-3-89318-084-4 on OpenProceedings.org. Distribution of this paper is permitted under the terms of the Creative Commons this data. license CC-by-nc-nd 4.0. • We suggest the Shift-Table approach for correcting a learned In basic implementations of binary search, the “hot keys” are index model, which complements a valid (monotonically cached with their payload and nearby records in the same cache increasing) CDF model by correcting its error. line, which wastes cache space. Binary search thus uses the cache • We show how, and in which circumstances, the suggested poorly and there are more efficient algorithmic approaches whose methods can be used for best performance. performance is not sensitive to data distributions. • We suggest cost models that determine whether the Shift- Cache-optimized versions of binary search, e.g., a binary search Table layer can boost performance. tree such as FAST [20], a read-only search tree that co-locates • The experimental results show that our suggested method the hot keys but still follows the simple bisecting method of bi- can improve existing learned index structures and bring nary search, are up to 3X faster than binary search [21]. This stable and almost-constant lookup time for real-world is because FAST keeps more hot keys in the cache and hence it data distributions. Our enhancement layer achieves up needs to scan a shorter range of records in the local search phase to 3X performance improvement over existing learned (cache-non-resident iterations of the search). indexes. More interestingly, we show that for non-skewed distributions, the Shift-Table layer is effective enough to 2.3 Preliminary Experimental Analysis help a dummy linear model outperform the state of the art learned indexes on real-world datasets For a tangible discussion and to elaborate on the real cost of a learned model, we provide a micro-benchmark that measures the cost of errors in a learned index. We use the experimental 2 MOTIVATION configuration used in the SOSD benchmark [21], i.e., searching 2.1 Lookup Cost for Learned Models over 200M records with 32-bit keys and 64-bit payloads. Figure 2a In modern hardware, the lookup times of in-memory range in- shows the lookup time of the second phase (local search) in a dexes and the binary search algorithm are mainly affected by learned model for different prediction errors. We include the their memory access pattern, most notably by how the algorithm lookup times for binary search, as well as FAST [20], over the uses the cache and the Last-Level-Cache (LLC) miss rate. whole array of 200M keys. Processing a range query in a learned index has two stages: We are interested to see that if the position predicted by a predicted_pos¹ º 1) Prediction: Running the learned model to predict the location learned index, say G , has an error Δ, then how of the first result for the range query; and 2) Local search (also long does it take in the local phase to find the correct record. Thus, known as last-mile search): searching around the predicted loca- for each query G8 , we pre-compute the ‘output’ of the learned »predicted_pos¹ º ± ¼ tion to find the actual location of the first result. Figure 1ashows index with error Δ, i.e., G8 Δ , and then run f »predicted_pos¹ º ± ¼g common search methods for the local search. If the learned model the benchmark given G8, G8 Δ tuples. can determine a guaranteed range area around the predicted po- As shown in Figure 2a, if the error of the model is more than ∼ sition, one can perform binary search.
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