Lecture 11 - Stochastic Optimisation Part 1 Flashcards
What is Stochastic Optimisation?
A framework for finding optimal solutions to problems where randomness or uncertainty is present in the objective function or constraints,
it uses randomness in their iterative steps to explore the solution space
Why do we use Stochastic Optimisation?
The function we are minimising is not known or not differential
What are the Advantages/Disadvantages of Stochastic Optimisation?
Advantage:
Works when deterministic or exact methods fail due to incomplete information.
Limitation:
Stochastic methods often require many evaluations
convergence is not guaranteed to a global optimum.
As part of the Blackbox what are the 3 requirements needed for optimisation?
Three core needs for optimisation:
1. A modelling language to describe candidate solutions.
2. Model - A way to execute and evaluate those solutions.
3. A performance metric to assess quality.
Why are the 3 requirements needed for optimisation important?
These are the minimal requirements for setting up any optimisation framework.
Why must you choose a good hypothesis space?
You must choose a good hypothesis space (the set of all possible solutions). If your solution isn’t even in the space, you can never find it.
What are the advantages/disadvantages for requirements needed for optimisation (BlackBox)
Advantage:
Flexible — supports different problem domains (e.g., scheduling, classification).
Limitation:
* Inefficient if done randomly.
* May never find a good solution if the hypothesis space is poorly chosen.
Define Heuristic
- Heuristics are strategies or “rules of thumb” that help guide the search process in a smarter way.
What is the Baseline Algorithm
Basic Operations (Baseline Algorithm)
1. Generate a candidate solution from the hypothesis space.
2. Evaluate how good that solution is (fitness, loss, score, etc.).
3. Repeat until good enough.
Why are Heuristics important for Baseline Algorithms?
Used in all optimisation algorithms
Helps to explore and improve algorithms
What are the limitations of Baseline Algorithm
Limitations:
* This naive version can be very inefficient.
* If the solution space is large or complex, the process might take forever, especially if sampling is done at random.
* There’s no guidance on where to search next — it’s like searching blindfolded.
What is the Incremental Improvement Heuristics?
Easier to find a good solution by modifying one you’ve already found than by starting from scratch each time
Why does Incremental Improvement Heuristics work?
Good solutions are near other solutions
Build on past experience
We get a path towards a better solution
What is Tweaking?
Tweaking = making small, informed changes to an existing solution.
Why do we use Tweaking?
Why:
* More efficient exploration of solution space.
* Assumes better solutions lie near existing good ones.
What are the advantages/disadvantages of Tweaking?
Advantage:
Explores locally with the potential to improve incrementally.
Limitation:
Depends on what “small change” means in a given space (not always obvious).
How do you apply Tweaking to Basic Operations?
To explore the solution space by changing (modifying) existing candidate solutions in order to find better ones.
Steps (from the slide):
1. Initialisation: Start with one or more solutions.
2. Assessment: Evaluate their quality (fitness, cost, error, etc.).
3. Modification: Make a copy and tweak it to form a new candidate.
Why do you modify the Basic Operation?
Starting from scratch each time ignores past knowledge. Tweaking is faster and often more effective.
What are the types of Tweaking modifications that can be applied?
○ Deterministic: Always the same tweak (e.g., move one step in gradient direction).
○ Stochastic: Introduce randomness (e.g., mutation in genetic algorithms, simulated annealing steps).
What are the advantages/disadvantages of Basic Operations with Tweaking?
Advantages:
* Efficient use of already-good solutions.
* Can converge quickly.
Limitations:
* Can lead to local optima if tweaks are too small or lack diversity.
* Needs a well-defined way to tweak meaningfully.
What are Basic Operations with Selection in regards to tweakng?
To intelligently choose which existing solution to modify next.
What additional components are needed for Selection?
Additional Components Needed:
1. Storing solutions:
○ Store past candidates and their performance.
○ May involve just the best-so-far, or a population (as in genetic algorithms).
2. Selection mechanism:
○ Choose a candidate to modify (based on fitness, diversity, or random chance).
What are some Selection Strategies?
Selection Strategies:
* Greedy/best-so-far: Modify the best current solution.
* Tournament selection: Randomly pick a few, choose the best of those.
* Roulette-wheel selection: Probabilistic selection based on fitness.
Why does Selection Matter?
- Without good selection, you might waste time tweaking bad solutions or get stuck tweaking only the best one repeatedly.
What are the advantages/disadvantages of selection?
Advantages:
Helps balance exploration (trying new areas) vs exploitation (refining known good areas).
Limitation:
Can still be misled by deceptive landscapes or noisy evaluations.
What does Selection and Tweaking lead to eventually?
Leads to:
A gradient-ascent-like behaviour without needing gradient information. You improve over time by selecting, tweaking, and replacing solutions — similar to what gradient ascent does, but using only feedback from evaluations.
