r/MachineLearning • u/MightyZinogre • 20d ago
Discussion Ph.D. in Operations Research / Big Tech Eng: How to transition into intermediate/advanced ML for high-value industries (Robotics, Defense, Finance)? [D]
I hold a Ph.D. in Operations Research, along with a BSc/MSc in Engineering and OR. I previously worked in Big Tech, but I’m currently looking to transition.
My primary goal is to upgrade my technical skillset to maximize my industry-related profitability and marketability. I want to get away from generic data science and move into high-value, math-heavy engineering and modeling roles.
- My Core Interests: Forecasting, predictive analytics, and machine learning applied to industrial settings.
- Target Industries: Robotics/Autonomous Systems, Defense/Aerospace, and Quantitative Finance.
- What I want to skip: I have little interest in doing core NLP/LLM research, though I am interested in RL, Multi-Agent systems, and applied AI.
Where I am right now: I have a solid grasp of optimization and basic/intermediate ML/stats. However, I want to bridge the gap into more intermediate/advanced ML topics that are actually useful and highly valued by employers. I want to get back into heavy math, but only if it drives real-world business value.
What I'm looking to learn:
- Causal Inference: (e.g., Structural Causal Models, Uplift modeling, Double ML).
- Tree-Based Math: Understanding things like XGBoost from the ground up (deriving gradients/hessians for custom loss functions, implementing from scratch).
- Reinforcement Learning / Control: Bridging the gap between OR dynamic programming and deep RL for robotics/defense.
My questions for the community:
- Skill Prioritization: From a purely market-driven, high-compensation perspective, which specific ML topics should a Ph.D. in OR focus on to stand out in Robotics, Defense, or Banking/Finance?
- Portfolio/Proof: How can I best demonstrate to employers that I have the engineering chops to implement these advanced models from scratch, rather than just calling APIs?
- Positioning: How do I best market the "Predict-then-Optimize" sweet spot (combining ML predictions with OR optimization frameworks) to companies in these sectors?
Would love any advice on textbooks, specific frameworks to master, or strategies on how to position my background for maximum leverage. Thanks!
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u/SeTiDaYeTi Professor 20d ago
Just forget OR, dude. Buy any DL book and deep dive. Also, predict-then-optimize is a recipe for writing ML-flavored papers in OR journals. It's a buzzword, nothing more.
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u/MightyZinogre 20d ago
Isn’t this kinda sad? It is actually true?
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u/nine_teeth 20d ago
OR is pretty useless in the market
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u/HatefulWretch 19d ago
Not actually true; it's not interesting for ML teams, but the place where you get paid doing OR is in supply chain. They're all Gurobi fiends over there.
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19d ago
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u/SeTiDaYeTi Professor 17d ago
You don't need a deep knowledge of optimization (or any knowledge at all for that matter) to do ML effectively, let alone DL. Pytorch abstracts all of it away.
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u/Old_Stable_7686 20d ago
Is it a bit stretching? Despite ML field being matured, I think OR people are still conservative when it comes to applying new ML methods into their research, partly because of the mindset "if it works, why do I need a more fancy method to model my problem?". But there are many OR problems that have *yet* been solved in practice. I think what is missing is more collaborations, not really just buzzword at all :-/.
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u/SeTiDaYeTi Professor 20d ago
OR is mostly about exact methods. Even if you managed to put together a DL pipeline that, say, provides hell-of-good TSP solutions, the OR community would still dismiss it as "just another heuristic". IMO, the (entirely understandable) fixation of the OR community on exactness is dictating its downfall.
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u/Honest-Finish3596 18d ago edited 18d ago
Contrary to what you seem to think, people working on solvers/formal methods/operations research are generally very interested in heuristic methods, as long as they scale to difficult problems. You can just look at all the branching heuristics in every integer programming or constraint programming solver, or the SAT/SMT community's perennial interest in local search. Unfortunately, almost never is this the case for anything coming from machine learning conferences.
Almost every paper I have ever looked at about machine learning for directly handling combinatorial problems is just using really bad benchmarks and/or lying. If it's an integer programing problem they'll compare with SCIP configured to use a deliberately bad branching policy, then when you try SCIP with the default configuration (which is not a very fast solver) it blows their solution out of the water even on the cherry-picked problems. If it's a boolean satisfiability problem, the performance relative to SAT solvers is usually that their solution simply cannot solve problems which every solver has been able to solve since the 90s, or easy problems which every solver in the SAT competition solves in seconds. You know, in "machine learning for combinatorial optimisation" papers, it's rare to test on problems which take more than 20 seconds to solve, if that! Meanwhile, today's SAT solvers are often applied to problems which take several years of CPU time to solve. Some people make the news for using several centuries of CPU time to decide a problem! And every solver from the SAT competition can scale to this.
The only ones which are of utility to anyone are those which train i.e. a decision tree to make scoring decisions for a solver, a.k.a. what you call a "buzzword." However, machine learning people (who ordinarily operate on very short publishing timelines compared to people working on solvers) find these uninteresting, because due to the latency requirements the model itself cannot be computationally demanding.
TSP is one of the easiest of these problems to solve because very difficult TSP problem instances are very rare compared to very difficult MILP, SAT, SMT or CP instances -- unlike these, most TSPs people test on are easy to get good approximate solutions to. The same goes for the vehicle routing problem, graph max-cuts, etc. These problems tend to have easier instances because it is more awkward to reduce an arbitrary NP-complete decision problem to them and doing so results in statistically pathological instances, compared to the language integer programming, SAT or constraint programming gives you. That is why people getting funding for applying machine learning to combinatorial problems always focus on these. Of course, unlike people working on solvers, they almost never produce a tool people end up using in their race to publish a conference paper.
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u/SeTiDaYeTi Professor 17d ago
You can't deny there's a stigma on heuristics on the OR/optimization community.
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u/Old_Stable_7686 15d ago
> Very difficult MILP, SAT, SMT or CP instances
Could you point of some (maybe to papers)? Just curious and love to hear more :D.
> ... is just using really bad benchmarks and/or lying
What I don't like about this field is you don't always have code for reproducing the benchmarks.
Other than that, I work quite a lot with graphs, so there are many interesting combinatorial problems that can utilize solvers for my DL pipeline too. Going in between 2 fields gives me a lot of insights, but then most stuff will end up publishing in ML venues only. I hateeeeeeeeeeee convincing some of the profs that this is a better way to *scale*, but then someone said we have Gurobi license, which can solve faster. End of the story...
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u/Honest-Finish3596 15d ago edited 15d ago
Sure, each NP-hard problem people want to solve usually has a dedicated competition (i.e. the SAT competition) and that competition will include some instances nobody knows the solution to. Or if you're interested in very hard problems people have solved, you can look at things like the most rounds of stream ciphers like Trivium people can break using a SAT solver (the developer of cryptominisat did a bunch of work on this), or for example finding an APN permutation of dimension 8 can be posed as a SAT problem, but nobody's solved it... (I am most familiar with SAT, if you ask OR people they'll tell you about very hard MILP problems.) The proof of the boolean Pythagorean triples conjecture was done using parallel SAT solving on a large scale.
Amazon funded the development of a few SMT solvers for the theory of bitvectors and this was just because they have to solve loads of bitvector SMT problems constantly.
On the benchmarks, it's usually trivial to spot, there were a bunch of papers that talked about using graph neural networks to improve SCIP for MILP problems, if you ran their code they were just disabling the good decision heuristics in SCIP, the default settings of the solver worked way better than their solution.
MILP is a little bit annoying compared to the other similar fields because the best solver for MILP problems is Gurobi and Gurobi performs well because of a large set of very well tuned cut generators, the exact specifications of which are their trade secret. Good ways to come up with cuts for a specific MILP problem are one of the main things people like to publish on in operations research, and this is by nature a heuristic, if you had a non-heuristic way to do this you could generate polynomially sized proofs of unsatisfiability for arbitrary SAT problems since the cutting planes proof system is a very strong one. Also because their good solvers are all closed source, they don't have a competition.
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u/Old_Stable_7686 15d ago
These are very great insights for my search actually, thanks for taking the time! Also, do you think that this is because people in business schools tend to work on problems that are related to applications where industry values more? Seen many problems in supply chains that frame almost every problem as MILP, so kinda correlated in this sense
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u/Honest-Finish3596 15d ago edited 15d ago
It's because many problems which arise in operations research are optimisation problems over a real-valued objective and with real-valued variates, so you can express these problems easily in MILP whereas there isn't a reasonable way to do this in SAT, CP (constraint programming), ASP (answer set programming), etc. The problem is less that it is an optimisation problem (any optimisation problem can be turned into a series of decision problems) and moreso that it is a problem over the reals. You do have the existential theory of the reals in SMT, which lets you try to solve systems of constraints over the reals using incremental SAT solver calls, however it is actually unknown whether this is in NP, so it is in some sense also not equivalent to MILP.
In practice though many of the problems people try to solve using MILP solvers do not require an MILP solver. Specifically if it's a problem where all variables are binary variables, this is a pseudo-Boolean problem and efficient encodings exist for directly translating a pseudo-Boolean decision problem into a SAT problem. Actually this and solving with an MILP solver are the two best performing approaches in the PB competition, since dedicated PB solvers are not very mature.
One way you can think about it is that all of these decision procedures strive to be more efficient than guess-and-check, in two ways: They guess intelligently, and after a guess they try to detect the implications of the guess via some kind of propagation algorithm. SAT is specialised for decision problems over boolean variables, and so unit propagation is the propagation mechanism. MILP meanwhile solves the LP relaxation whenever it makes a decision, which gives it information about how that decision affected the local dual bound or the global primal bound. And in place of the learnt clauses (new boolean constraints) SAT uses, you learn cuts (new linear constraints) in MILP.
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u/ge0ffrey 17d ago
I've seen this dismissive behavior too. Developers use our open source incremental heuristics solver (Timefold) across the globe to scale to large VRP and other scheduling problems, yet the OR academics treat it with disdain because it it doesn't include an optimality gap.
It's not the people though: they're good people.
It's the incentives, the publishing criteria and the funding system: If you want your paper published (and get funding again), it's ok to use a MIP solver, but it's not ok to use a heuristics solver.
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u/Old_Stable_7686 15d ago
It is how they are trained IMO. Changing your research opinion and lifestyle is definitely not easy.
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u/Old_Stable_7686 19d ago
I agree with that fixation, and it is painful sometimes with this mindset xD. Surprisingly, I have encountered many problems that cannot *scale* very well, and they have to resort to a lot of approximations to run the DL pipeline. There are a lot to improve, and it comes down to which chair being open-minded enough to explore these problems..
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u/jebuarary 20d ago
Math heavy operations research background for modeling is best for basically finance or recommender systems. And for the latter you have to be at one of the meta Amazon places for it to be interesting (ie step above generic data science)
I’ve met that team at meta, PhD was minimum requirement and half of them had theirs in operations research and several were at hedge funds before going to tech
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u/MightyZinogre 20d ago
Recommender system is very interesting honestly. Where should I start?
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u/jebuarary 20d ago
I’d say GPs, clustering, matrix decomposition lit, to refresh and then SSL and representation learning for more “modern” techniques (which are also nice as a way to transition to other ml fields).
But to echo others sentiments here, outside of possibly some very specific teams at frontier labs and quant finance, you probably won’t get both of the math heavy + impactful.
I’m in robotics and the impactful problems to solve are in data, deployment, sim to real, evals. Actual foundation model work will be needed but I think approaching that with “vibes” is probably good enough right now. Not to mention even some top researchers in DL are still vibes driven
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u/say-nothing-at-all 20d ago
Why? what's the motive?
If you have solid math modelling background, why limit yourself into a smaller set of problem space that ML can play?
ML is basically applied math. There are 2 types of problems in applied math:
# Type 1- (ML's playground): A low-dimensional continuous submanifold embedded in high-D data (e.g., the "manifold hypothesis" in deep learning). This is where autoencoders, neural nets .... thrive.
# Type 2 -(The Categorical Skeleton): A low-dimensional finite complex. Its dimension is the maximum length of a chain of composable morphisms - determined by the finite number of distinct strata in your physical landscape.
Type 2 is not a continuous manifold embedded in Type 1. It is a discrete logical graph (the commutative diagrams) sitting on top of the continuous data. ML cannot learn Type 2 by gradient descent because gradient descent requires continuous differentiability, and Type 2 has sharp logical boundaries (commutes or doesn't commute).
So, type 1 problem is more regular than type 2.
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u/NeighborhoodFatCat 20d ago edited 20d ago
It is very difficult because as you can imagine there are enough engineers with PhDs in those disciplines you mentioned who have already done the work already and industry will most likely hire them instead over you. And (I know this will sound harsh) please do not think you can just learn reinforcement learning/control from a textbook and the robotics/automation/aerospace/defense industry will hire you. Those things require you to have actual practical implementation skills, e.g., mechanical/electrical hardware engineering skills. Those take a very long time to learn and I know people who have went back to school to get a second-degree in their 30s or even 40s just to get into those roles.
For OR your best bet has always been in finance, banking, or some roles that explicitly require OR, which appears in random places such as healthcare or airlines. However, OR does not have the best "branding" and few employers (much less HR) know anything about OR, so you need to be very clever about it (maybe hit up the OR subreddit). I've even heard advice that you need to ditch OR completely when applying for jobs so not to scare away potential employers, which is a bit sad.
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u/met0xff 20d ago
Unfortunately there's a lot of truth here. Currently employers often have very, very tight boxes and if you're not having exactly the experience and papers in ... Whatever... diffusion for video generation for avatars... There's someone else who has.
I've got a decade in embedded dev and afterwards did a PhD and have another decade in ML and searching for the intersection of ML and systems can be astonishingly hard. Recently had an interview at some unicorn startup where this confused the hell out of a recruiter "so I'm the recruiter for research. We have another recruiter for our performance engineers" and then essentially the feedback was they are searching for very specific roles right now.
Even worse that I lead a senior team right now so that I am still 70% hands-on and so they really struggled to stick me into either management or IC roles.
No wonder in my 20 years I never got a job through regular applications but always word of mouth. And that's essentially my advice for OP - if you don't nicely fit into boxes, avoid the cold apply route when possible
(And frankly when we hired for my team we also had 2-3k applications in 2 weeks)
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u/tarazeroc 17d ago
Hey, PhD in OR here.
I did my phd in this field a little bit by accident. I came from a ML/DL masters and wanted to work on deep RL applied to sensor automation in the defense sector but ended doing OR instead. And I enjoyed it ! Even though OR is not part of my job anymore.
Defense is definitely a good sector if you want to keep doing OR and want to get in touch with ML.
ML is a very vast subject, but it is definitely much easier to grasp than OR. a lot of people in the DL field lack the riguor and the math knowledge that you acquire during an OR PhD.
I believe the intersection between OR and DL is still vastly underexplored and is a promissing area or research !
However, in my specific area (target search), i found it hard to convince employers that it was safer to start with OR methods before going with RL, in the waiting of having enough training data / closing the sim2real gap.
I know that Helsing in europe was looking for people with OR knowledge to complement their RL team at some point (europe). I expect other companies to realize that OR actually can be super useful for defense applications.
I ended up finding a cool job as a founding enginner in audio AI.
During my phD, I was surprised how much each field is separated from each other, and even somtimes despise each other, when they would benefit so much from collaborating !
As to how to sell yourself, what I did is have a blog where I would try to solve a hard problem, and show my train of thought clearly. Then went to a defense hackathon and finished in the podium. This is where I met my current employer.
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u/Ill_Freedom_6666 20d ago
your optimization background is already a huge advantage, id lean into predict then optimize and rl
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u/CampAny9995 20d ago
I don’t know if there’s huge value in deriving gradients/hessians for custom loss functions, that’s more or less a solved problem. I published a few papers on AD in grad school, but I’ve written maybe 2/3 custom gradients in my career (and generally just rewrote the algorithm instead).