Explainable Linear Programs

https://www.jeremykun.com/shortform/2025-02-06-2124/

by matt_d • 1 year ago

98 31 1 year ago

Article entitled "Explainable Linear Programs" doesn't explain a linear program, nor link to an explained linear program.

mjburgess• 1 year ago

It seems more of an internal note to a research community about what should be published/researched, rather than anything informative.

nerdponx• 1 year ago

2nd paragraph:

A linear program is a mathematical model that defines some number of variables, linear constraints, and a linear objective function. When some variables are forced to be integer (ILPs), you can solve a lot of useful problems like scheduling, routing, and packing. That’s basically how all supply chain optimization works.

The author clearly expects the audience to know what an "objective function" is (it's something that you want to optimize, e.g. minimizing fuel on a delivery route).

Furthermore:

Fast forward to today, when my colleague pointed me to this 2023 paper by Microsoft researchers Beibin Li, Konstantina Mellou, Bo Zhang, Jeevan Pathuri, and Ishai Menache, “Large Language Models for Supply Chain Optimization”. They basically did the same thing as me, but added an LLM to convert natural language queries to their structured query language. The colleague who pointed me to this was working on a similar idea.

The author isn't showing examples of their idea, because another group did the same thing but arguably better, so they linked to that paper instead.

tsumnia5• 1 year ago

Shamelessly Plugging my own videos on Linear Programs and Meta-heuristic Algorithms to solve Linear Assignment Problems.

The Linear Assignment Problem: https://www.youtube.com/watch?v=dMJpCnocmGk

Simulated Annealing: https://www.youtube.com/watch?v=21EDdFVMz8I

Genetic Algorithms: https://www.youtube.com/watch?v=Jm4qGteDlZE

Ant Colony Optimization: https://www.youtube.com/watch?v=Jm4qGteDlZE

Whenever I find some mythical free time I'd like to add a video about Constraint Satisfaction, but in the mean time here's my full lecture on CSP: https://www.youtube.com/watch?v=w5tPsbOvkmU

When we think about Explainable AI, we're looking for a "reason the AI made a decision". LLMs are using text prediction to make their decisions, but more traditional AIs use a different heuristic for their selection process. Many of these methodologies are still in use today and get the job done quite well. The "explanation" for these AIs is a (hopefully) intuitive method inspired by other natural phenomena that occurs in the world (like evolution, blacksmithing, literally how ants move).

If however you're looking for AI to explain the "why" element, I will admit that is where the traditional algorithms struggle, but I would add that LLMs aren't much more informative. Its reflection is going to be by guessing what the next right word to say is, which isn't any better or worse than the other models in terms of explainability.

te2• 1 year ago

Watched your Linear Assignment video, and the whole time I'm thinking why would one ever contemplate a meta-heuristic for Linear Assignment when Hungarian/Munkres runs in polynomial time? I think I must be missing some context.

rramadass2• 1 year ago

Can you recommend some good books which explain "Mathematical Programming/Optimization" from the very beginning in a simple manner? Most books are notation heavy and seem to lack explanations for the beginning student. Long ago i was recommended N.S.Kambo's Mathematical Programming Techniques which covers a lot of ground but is very hard to understand.

The second question is, how (and where) are these techniques used in the ML/AI domain?

firesteelrain5• 1 year ago

I wrote a research paper on a novel use (or so I thought) of Linear Programming for how to optimize selection of cloud resources. The feedback I received was that application of LP in a newish area is not publishable and does not cover new ground. So don't write research papers about a new application of LP. It still covers the known and common cases of LP. No new ground to cover here.

Knowing that and thinking about it more a couple years later, what the author seems to be describing is akin to BDD approach to LP model generation as an intermediary language before you get to the actual LP model. In this case, that approach is overshadowed by the use of LLMs.

Use of LLMs to generate English language is no longer novel nor new. Therefore, any application of LLMs that do that aren't novel either.

tptacek• 1 year ago

Got a draft of it?

whatever13• 1 year ago

Probably you need to submit to a different journal. It is not indeed a theoretically interesting contribution but it is definitely a very interesting practical application. Many journals would welcome your contribution.

firesteelrain5• 1 year ago

It was to IEEE. Maybe that was hard mode? It was for a Cloud Conference in 2023.

One of the comments

“ This paper shows a linear programming problem to address cloud security. It's not clear why the LP program addresses security. Comparison with SOTA is also lacking.”

“ The paper attempts a fresh perspective on Cloud Security Decisions using a well-known approach.

Unfortunately, as currently presented, it does not deliver any significant research results, and thereby its contribution is limited.

The paper as formulated is closer to a vision paper -- not that it actually is -- than to a research paper. This reviewer notes the limited results. No surprises, the paper is also missing an evaluation analysis of the results.”

I had evaluation of results. I had never heard of a vision paper.

t_mann2• 1 year ago

Fyi, it's quite common to have a paper rejected on the first (couple of) submission(s). With feedback along the lines of "not interesting enough", it's usually worth it trying it again somewhere else. Sounds like that venue was looking for methodological innovation within optimization, you could try it at a more domain-oriented outlet that would appreciate how your solution improves upon the SOTA for cloud resource selection.

What I'm also saying: just because you had a paper rejected once with a specific comment doesn't mean that every other paper where such a comment could vaguely fit needs to be rejected as well.

firesteelrain5• 1 year ago

I had several comments. I posted below but here are some

This was my first and only research paper submission under my MS in Systems Engineering. It wasn’t a requirement but the department head was impressed that any Masters student might try to submit at all.

It was to IEEE. Maybe that was hard mode? It was for a Cloud Conference in 2023.

One of the comments

“ This paper shows a linear programming problem to address cloud security. It's not clear why the LP program addresses security. Comparison with SOTA is also lacking.”

“ The paper attempts a fresh perspective on Cloud Security Decisions using a well-known approach. Unfortunately, as currently presented, it does not deliver any significant research results, and thereby its contribution is limited. The paper as formulated is closer to a vision paper -- not that it actually is -- than to a research paper. This reviewer notes the limited results. No surprises, the paper is also missing an evaluation analysis of the results.”

I had evaluation of results. I had never heard of a vision paper.

This was one of the better comments that actually provide the best feedback. The section that they mention was exceptionally long was my literature review:

“ This paper describes the idea of leveraging linear programming to determine how to allocate security resources in the cloud.

It would be better if the paper focused more on describing the proposed solution. The current description in Sec III is insufficient. First, there are many assumptions that were made to explain and formulate the linear programming for security resource allocation. These assumptions need to be explained further, e.g., to provide information on parameterizing values such as the budget and weights. Second, it would be better if the paper describes the system models based on a current cloud service provider so that the discussion is more concrete.

The implementation section can be reduced significantly, e.g., the Sec V.B. can be condensed to only show important lines of code.

There is no evaluation of the proposed solution. It is hard to assess how well the proposed solution will work without evaluating the formulation based on existing cloud service providers. Additionally, it is important to choose some baselines to compare the proposed solution.

The related work section takes 2 out of the 6 pages and feels unnecessarily long. It might be sufficient to describe how prior work solves this problem and how this paper differs.

A final remark is about the problem formulation. It is unclear what the challenges of allocating security resources are and how those challenges differ from other cloud-based resource allocation problems.”

darksaints• 1 year ago

The reason why application of LP in a newish area is not really publishable is because the field of Operations Research has been doing that continuously for the past 80 years. Modeling planning problems as mathematical optimization problems has been done long before computers were capable of solving them, and convex optimization problems in particular have the most historical work put into them, due to early innovations. Optimizing selections of cloud resources in particular is so ubiquitous that those exact types of problems tend to be used as tutorials to get people up to speed for various types of solvers.

Unfortunately we have a very bad branding problem, and almost nobody who hears the name "Operations Research" can infer what we actually do from the name, let alone understand the mountains of research that we've accumulated over time.

moussore• 1 year ago

No offense to the author, but there's a wealth of research (and tools) out there on this subject - robust optimization, stable theory, etc. (not requiring LLMs and ML buzzwords)

sevensor• 1 year ago

it’s basically not publishable as research

I was surprised he said this, since it sounds like he’s doing sensitivity analysis, which has been a thing for longer than I’ve been alive.

j2kun2• 1 year ago

IMO it's not sensitivity analysis in the classical sense because the explanations people are looking for are not about slight perturbations of the model, but usually more drastic ones. I found that, for example, the dual of an ILP is completely useless for explanation purposes. Stuff like "shadow prices" are just not relevant for complex formulations that model supply chain dynamics.

If there is useful theory here, I'd love to hear about it, but it's not in any textbooks I've read.

j2kun2• 1 year ago

Could you give some examples of tools that people use to automate explanation of linear programs?

NBJack• 1 year ago

Please share; I'm super interested in ways I can apply these concepts to a related work, and I have already heard from at least individual whom believes MIP explainability is 'impossible'.

taeric• 1 year ago

Hard not to feel that most of this research has been lost on the modern practitioner? I'd wager even money that a sizeable portion of new entrants to programming are not even aware of optimization techniques. Never mind if they are familiar with them.

Nor is this limited to optimization techniques. State machines are surprisingly ignored by many.

Makes me think this would be a fun post. What are the techniques that are basically ignored by most current discourse?

rahulnair23• 1 year ago

Pointers to said tools would be beneficial. Robust optimization is somewhat different from what the author states.

Explainable Linear Programs

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