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optimization

nounAlso: optimisation, mathematical optimization, mathematical programming, optimize

In plain wordsFinding the best possible choice according to some score, such as the lowest error or the highest reward. Training an AI is optimization: adjusting its settings until its mistakes are as small as possible.

  1. 1

    The task of choosing values for some variables — a model's parametersparameter, n.: One of the adjustable numbers inside an AI model that are tuned during training. Large language models have billions of them, and together they store what the model has learned., a route, a schedule — that make an objective functionobjective function, n.: The score that an optimization process tries to push as low, or as high, as possible. For an AI, it defines what 'doing well' means during training. as small or as large as possible, often within constraints; also the branch of applied mathematics devoted to such problems and the algorithms that solve them. Which method fits depends on the problem's shape: whether the variables are continuous or discrete, whether constraints apply, and whether the objective is convexconvex optimization, n.: Finding the lowest point of a bowl-shaped landscape. Because a bowl has only one bottom, such problems can be solved reliably — unlike training a neural network, whose landscape is bumpy., smooth or stochasticstochastic, adj.: Involving chance, so the same starting point can lead to different outcomes. AI chatbots are stochastic: ask the same question twice and you may get two different answers.. Machine learning is largely optimization: training minimizes a loss functionloss function, n.: A score that measures how wrong a model's predictions are. Training means adjusting the model, step by step, to push this number down. plus regularization over a model's parametersparameter, n.: One of the adjustable numbers inside an AI model that are tuned during training. Large language models have billions of them, and together they store what the model has learned., almost always with first-order methods driven by the gradientgradient, n.: A list of slopes showing which way, and how steeply, a quantity rises as each of its inputs changes. Training nudges an AI's settings in the opposite direction, downhill. — stochastic gradient descentstochastic gradient descent, n.: A faster version of gradient descent that estimates which way is downhill from a small random sample of the training data at each step, instead of checking the whole dataset., AdamAdam, prop. n.: The most widely used method for training neural networks. It smooths the direction of updates over time and automatically sets a separate step size for each setting based on how large its recent changes have been. and their relatives — because the problems are huge, non-convex and noisy. Hyperparameter tuninghyperparameter tuning, n.: Trying out different settings for a model's training, such as learning speed or model size, and keeping the combination that performs best on data held back for checking. and Bayesian optimizationBayesian optimization, n.: A smart way to tune settings when each test is expensive: build a statistical guess of how settings affect results, then try whichever setting that guess says is most promising next. optimize black-box functions, and reinforcement learningreinforcement learning, n.: A way of teaching a computer program by trial and error: it tries actions, earns points for good results and penalties for bad ones, and gradually learns which choices pay off over time. maximizes expected returnreturn, n.: The total reward an AI agent collects from now until the end of a task, usually counting near-term rewards more than distant ones. Agents are trained to make this total as large as possible.. Learning differs from pure optimization because the real goal is low error on unseen data (generalizationgeneralization, n.: How well a model copes with new examples it has never seen, rather than just memorizing its training data, like a student who understands the method, not just the answers.), not just on the training set.

    The optimization diverged twice, so we lowered the peak learning rate.

  2. 2

    Software engineering

    Changes that make a program, model or system faster, cheaper or smaller without changing what it computes, as in compiler optimizations or inference techniques such as quantizationquantization, n.: Storing an AI model's numbers with fewer digits, like rounding prices to the nearest dollar, so the model takes less memory and runs faster, usually with only a small loss of accuracy., kernel fusionkernel fusion, n.: Merging several small calculation steps into one, so a chip finishes them in a single pass instead of saving and reloading data in between, like cooking at the counter without returning ingredients to the fridge after each step. and KV cachingKV cache, n.: A memory store where a chatbot keeps its working notes on everything already read and written, so each new word does not require re-reading the whole conversation from scratch..

x∗=arg⁡min⁡x∈Cf(x)x^{*} = \arg\min_{x \in \mathcal{C}} f(x)

Origin

Calculus-based optimization goes back to Pierre de Fermat's method for maxima and minima (1630s) and to Lagrange's multipliers (1788); Augustin-Louis Cauchy proposed gradient descent in 1847. Leonid Kantorovich (1939) and George Dantzig, whose simplex method dates from 1947, founded linear programming and with it 'mathematical programming' as a discipline. 'Optimization' gradually displaced that name: the Mathematical Programming Society became the Mathematical Optimization Society in 2010.

Related

See also
  • objective functionobjective function, n.: The score that an optimization process tries to push as low, or as high, as possible. For an AI, it defines what 'doing well' means during training.
  • convex optimizationconvex optimization, n.: Finding the lowest point of a bowl-shaped landscape. Because a bowl has only one bottom, such problems can be solved reliably — unlike training a neural network, whose landscape is bumpy.
  • gradient descentgradient descent, n.: A method for training models by repeatedly nudging every setting a small step in whichever direction most reduces the error, like a hiker who cannot see the valley but keeps stepping wherever the ground tilts down.
  • loss functionloss function, n.: A score that measures how wrong a model's predictions are. Training means adjusting the model, step by step, to push this number down.
  • local minimumlocal minimum, n.: A spot lower than everything immediately around it, like the bottom of a small valley, even though a deeper valley may exist somewhere else.
  • stochastic gradient descentstochastic gradient descent, n.: A faster version of gradient descent that estimates which way is downhill from a small random sample of the training data at each step, instead of checking the whole dataset.
  • Lagrange multiplierLagrange multiplier, n.: A mathematical device for finding the best answer when strict rules must be obeyed: each rule becomes an extra price that grows when the rule is broken.
Contrast with
  • generalizationgeneralization, n.: How well a model copes with new examples it has never seen, rather than just memorizing its training data, like a student who understands the method, not just the answers.

Mentioned in

gradient descentgradient descent, n.: A method for training models by repeatedly nudging every setting a small step in whichever direction most reduces the error, like a hiker who cannot see the valley but keeps stepping wherever the ground tilts down., convex optimizationconvex optimization, n.: Finding the lowest point of a bowl-shaped landscape. Because a bowl has only one bottom, such problems can be solved reliably — unlike training a neural network, whose landscape is bumpy., linear programminglinear programming, n.: A mathematical way to find the best use of limited resources, such as a factory's machines or an airline's crews, when every cost and limit scales in simple proportion: twice the output needs twice the input., objective functionobjective function, n.: The score that an optimization process tries to push as low, or as high, as possible. For an AI, it defines what 'doing well' means during training., satisficingsatisficing, n.: Choosing the first option that is good enough instead of searching for the very best one — a sensible strategy when time, information or brainpower are limited., integer programminginteger programming, n.: Finding the best plan when some decisions must be whole numbers or yes-or-no choices — you cannot open half a warehouse or send 2.7 trucks. That small change makes the best plan far harder to find., Lagrange multiplierLagrange multiplier, n.: A mathematical device for finding the best answer when strict rules must be obeyed: each rule becomes an extra price that grows when the rule is broken., mild optimizationmild optimization, n.: Building an AI that settles for a solid result instead of squeezing out every last bit of score, since the most extreme ways to max out a goal are often loopholes or excesses nobody wanted., quantilizerquantilizer, n.: An AI decision rule that, instead of picking the single highest-scoring action, picks at random among the top few percent of ordinary, human-like actions — limiting how badly a flawed goal can backfire., variational inferencevariational inference, n.: A way of approximating a hard-to-compute probability distribution by picking the closest match from a simpler family of distributions, turning a hard problem of adding up every possibility into an optimization problem.