Machine Learning for Combinatorial Optimization: A Methodological Tour d'Horizon

Machine Learning for Combinatorial Optimization: A Methodological Tour d'Horizon Yoshua Bengio Andrea Lodi Antoine Prouvost

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Machine Learning for Combinatorial Optimization: A Methodological Tour d'Horizon 2021 European Journal of Operational Research / arXiv 10.1016/j.ejor.2020.07.063 1811.06128 bengio2021-ml-combinatorial bengio2021-ml-combinatorial.txt, the project's staged copy 5435bec785bae157189c79288fd9e5a690ac8992 arxiv-open operations-research

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them method Quotation withheld because this record is not cleared for redistribution. machine learning for combinatorial optimization Quotation withheld because this record is not cleared for redistribution. review review Quotation withheld because this record is not cleared for redistribution. mechanisms HANDCRAFTED HEURISTICS ARE SAID TO FILL TWO DIFFERENT GAPS, AND ONE OF THEM IS DEFINITIONAL: state-of-the-art algorithms rely on handcrafted heuristics for decisions that are otherwise TOO EXPENSIVE TO COMPUTE OR MATHEMATICALLY NOT WELL DEFINED. The craft is standing in both for intractability and for the absence of a definition, and the two are named in one breath Quotation withheld because this record is not cleared for redistribution. mechanisms A FIELD IS INTRODUCED WITH TWO NAMES IN ITS FIRST SENTENCE: Quotation withheld to assist military planners. One discipline, two labels, and the second belongs to a different literature about this quote: RE-SLICED. The acceptance footnote and licence notice are spliced INTO this sentence - "to use mathematics and computer science * Accepted to the European Journal of Operations Research. c(cid:13)2020. Licensed under the Creative Commons cbnd 1 to assist military planners" - so it cannot be quoted whole. The naming is at its head. 'c(cid:13)' is a copyright symbol that failed to map. Quotation withheld because this record is not cleared for redistribution. mechanisms THE PAPER'S MAIN MOVE IS A RE-DESCRIPTION OF ITS OBJECTS AS SOMETHING ELSE: a main point is SEEING GENERIC OPTIMIZATION PROBLEMS AS DATA POINTS, and then INQUIRING WHAT IS Quotation withheld task. Problems become instances drawn from a distribution, and that shift is the contribution Quotation withheld because this record is not cleared for redistribution. mechanisms AN APPARENT CONTRADICTION BETWEEN A COMPLEXITY CLASS AND PRACTICE IS POSED AS THE PAPER'S OPENING QUESTION: for these problems IT IS CONSIDERED UNLIKELY that a polynomial-time algorithm exists - HOWEVER, IN PRACTICE, the algorithms solve instances with up to millions of variables and constraints - HOW IS IT POSSIBLE TO SOLVE NP-HARD PROBLEMS IN PRACTICAL TIME? The category and the practice disagree, and the disagreement is the subject Quotation withheld because this record is not cleared for redistribution. mechanisms WHAT IS TO BE AUTOMATED IS DESCRIBED AS UNWRITTEN, AND A PARENTHESIS CONCEDES IT MAY NOT EXIST: the aim is TO AUGMENT AND AUTOMATE THE UNWRITTEN EXPERT INTUITION **(OR LACK OF)** on various existing algorithms. Three words in brackets admit that the target of the automation might be absent, and the sentence continues as though it were not in doubt Quotation withheld because this record is not cleared for redistribution. mechanisms A DEFINITION IS DECLINED FOR THREE TRACTABILITY REASONS AND NONE OF THEM IS IMPOSSIBILITY: explicitly defining what makes an instance A LIKELY ONE for the company IS TEDIOUS, DOES NOT SCALE, AND IT IS NOT CLEAR HOW IT CAN BE LEVERAGED when writing the algorithm - so the definition is replaced by a wish to AUTOMATICALLY SPECIALIZE. The reasons for not defining are practical, and the paper says so plainly Quotation withheld because this record is not cleared for redistribution. mechanisms HUMAN TRIAL-AND-ERROR IS NAMED AS A LEAKAGE CHANNEL, WHICH IS WHY A COMPARISON NEEDS INDEPENDENT DATA: as for ALL such algorithms, A FAIR COMPARISON can only be done on AN INDEPENDENT DATASET of instances - BECAUSE THROUGH HUMAN TRIALS AND ERRORS, THE DATA USED WHEN BUILDING THE ALGORITHM LEAKS INTO THE DESIGN OF THE ALGORITHM, even without explicit training. The designer is a fitting procedure about this quote: RE-SLICED, AND MY OWN CUT-WORD GUARD IS WHAT CAUGHT IT. My first end key was "...even without e" - which is where a 240-character DEBUG PRINT had truncated the sentence while I was searching the file. I used the output of my own truncated display as a key. The guard refused it, and the real text is "even without explicit learning components". Slice from the FILE, never from a print of the file. Quotation withheld because this record is not cleared for redistribution. mechanisms THE BASELINE IS SHOWN TO SHARE THE WEAKNESS BEING CHARGED AGAINST THE NEW METHOD: learned algorithms may be expected to FAIL ON UNSEEN INSTANCES TOO FAR FROM TRAINING - and IT IS ALSO WORTH NOTING that TRADITIONAL algorithms MIGHT NOT EVEN WORK CONSISTENTLY across all instances of a problem family, but TEND TO BE MORE ADAPTED TO PARTICULAR STRUCTURES. The complaint turns out to describe the incumbent as well Quotation withheld because this record is not cleared for redistribution. mechanisms A STANDING DIFFICULTY IS ATTRIBUTED TO A FUZZY DISTINCTION BETWEEN TWO DESCRIPTIONS OF ONE THING: generalization REMAINS A CHALLENGING TOPIC, PROBABLY BECAUSE OF THE FUZZY DISTINCTION BETWEEN A MULTI-TASK SETTING AND A LARGE ENVIRONMENT ENCOMPASSING ALL OF THE TASKS. The obstacle is not a missing result but an unresolved choice of description Quotation withheld because this record is not cleared for redistribution. mechanisms THE GRANULARITY OF A CATEGORY IS PRESENTED AS A DECISION WITH NO PRINCIPLED ANSWER, AND THE EXAMPLE IS CONCRETE: CHOOSING HOW AMBITIOUS ONE SHOULD BE IN DEFINING THE CHARACTERISTICS OF THE DISTRIBUTION IS A HARD QUESTION - if the company expands to other cities, SHOULD THEY BE CONSIDERED AS SEPARATE DISTRIBUTIONS, and one policy learned per city? Where one category ends and the next begins is a question the framework does not answer about this quote: EXTENDED: the first cut stopped before "and learn one branching policy per city?", which the tag depends on - the question mark carries the whole force of the point. Quotation withheld because this record is not cleared for redistribution. mechanisms THE SURVEY'S OWN CATEGORIES ARE DISCLAIMED AS NEITHER DISJOINT NOR EXHAUSTIVE, WHILE BEING USED: the Quotation withheld A taxonomy offered with its two standard failure modes conceded and the word NATURAL doing the justifying Quotation withheld because this record is not cleared for redistribution. in imitation-learning settings, performance is bounded by the (possibly suboptimal) expert what this limits: every imitation-learning result: Quotation withheld - it cannot exceed what it imitates Quotation withheld because this record is not cleared for redistribution. learned algorithms may not generalize to unseen problem instances what this limits: any generalisation claim: the learned algorithm Quotation withheld Quotation withheld because this record is not cleared for redistribution. The literature surveyed is early-stage rather than mature, so the survey reports directions rather than settled algorithms. what this limits: the standing of the survey's conclusions: THE LITERATURE WE SURVEY IS EXPLORATORY, I.E., WE AIM AT HIGHLIGHTING PROMISING RESEARCH DIRECTIONS ... INSTEAD OF RE[porting settled results] Quotation withheld because this record is not cleared for redistribution. Unsupervised learning is excluded from the survey. what this limits: the coverage of the survey: unsupervised learning is excluded Quotation withheld because this record is not cleared for redistribution. The treatment of imitation learning is a simplification of the ML literature. what this limits: the imitation-learning material as a guide to that literature: THE PART OF IMITATION LEARNING PRESENTED HERE IS LIMITED COMPARED TO THE CURRENT LITERATURE IN ML Quotation withheld because this record is not cleared for redistribution. Choosing which learning algorithm will perform best is outside the scope of the proposed methodology. what this limits: any use of the methodology to choose between algorithms: IDENTIFYING WHICH ALGORITHM WILL PERFORM BEST IS AN OPEN RESEARCH QUESTION UNLIKELY TO HAVE A SIMPLE ANSWER, AND IS OUTSIDE OF THE SCOPE OF THE METHODOLOGY PRESENTED HERE Quotation withheld because this record is not cleared for redistribution. The expert decisions the learned models are fitted to are stated to be, in part, mathematically not well defined. what this limits: a learned replacement for a solver heuristic: the decisions in question are ones that are either too expensive to compute or mathematically not well defined, so for some of them there is no formal target the model could be right or wrong about Quotation withheld because this record is not cleared for redistribution. The distribution the method is supposed to learn cannot be characterised, so a finite set of collected instances silently becomes the definition of the problem class. what this limits: a claim that a learned CO algorithm solves a problem class: the true distribution is unknown and cannot be characterised explicitly, so what is learned is whatever a finite collected set - for instance a company's historical instances - happens to contain Quotation withheld because this record is not cleared for redistribution. The quantity that defines success is stated to be inaccessible, and every reported figure is an estimate of it on held-out data. what this limits: any reported generalization error: the objective it estimates remains inaccessible, so the number is the model's performance on a particular held-out set and not the property itself Quotation withheld because this record is not cleared for redistribution. using machine learning to learn heuristics for combinatorial optimization problems Quotation withheld because this record is not cleared for redistribution. combinatorial optimization combinatorial optimization Quotation withheld because this record is not cleared for redistribution. heuristic heuristic Quotation withheld because this record is not cleared for redistribution. generalization error generalization error Quotation withheld because this record is not cleared for redistribution. overfitting overfitting Quotation withheld because this record is not cleared for redistribution. capacity capacity Quotation withheld because this record is not cleared for redistribution. test dataset test dataset Quotation withheld because this record is not cleared for redistribution. generalizing - THE INFORMAL SENSE: performance stays similar between the instances used for learning and unseen ones, which is how the word is used throughout the survey Quotation withheld because this record is not cleared for redistribution. generalize - THE FORMAL SENSE, AGAINST SOMETHING INACCESSIBLE: low values of the empirical objective translating into low values of the true one, where the true one cannot be computed and is estimated on a test set instead Quotation withheld because this record is not cleared for redistribution. the distribution of problems - AS WHATEVER WAS COLLECTED: unknown, not explicitly characterisable, and represented in practice by a finite set of historical instances, which is what the learned algorithm actually fits Quotation withheld because this record is not cleared for redistribution. builds-on → machine learning (from CS/AI) Quotation withheld because this record is not cleared for redistribution. capacity —causes→ overfitting capacity overfitting strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. generalization error —operationalised-as→ test dataset generalization error test dataset strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. millions — scale CO solvers reach in practice Quotation withheld because this record is not cleared for redistribution. 2 — ways ML can improve a CO algorithm Quotation withheld because this record is not cleared for redistribution. 2 — survey axes the paper derives Quotation withheld because this record is not cleared for redistribution. ML is a natural candidate to replace hand-crafted heuristic decisions Quotation withheld because this record is not cleared for redistribution. adding learning need not compromise overall theoretical guarantees about this quote: QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. the surveyed CO problems are NP-hard Quotation withheld because this record is not cleared for redistribution. generic optimization problems can be treated as data points Quotation withheld because this record is not cleared for redistribution. decision variables decision variables Quotation withheld because this record is not cleared for redistribution. distribution of problem instances distribution of problem instances Quotation withheld because this record is not cleared for redistribution. policy policy Quotation withheld because this record is not cleared for redistribution. combinatorial optimization (CO) combinatorial optimization (CO) about this quote: QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. traveling salesman problem (TSP) traveling salesman problem (TSP) Quotation withheld because this record is not cleared for redistribution. generalizing generalizing Quotation withheld because this record is not cleared for redistribution. operations research operations research Quotation withheld because this record is not cleared for redistribution.

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