Master algorithm design and upper bound proof

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SUMMARY

The discussion centers on mastering algorithm design and upper bound proof in the context of online learning. The user seeks assistance with a past exam question involving loss calculation for an online sequence of data, specifically using the formula $Loss(S) = \sum_{t=1}^{m} |y_{t} - \hat{y_{t}}|$. The conversation emphasizes the importance of sharing progress to facilitate effective help. Participants are encouraged to provide their current understanding and attempts to solve the problem for better guidance.

PREREQUISITES
  • Understanding of online learning algorithms
  • Familiarity with loss functions in machine learning
  • Knowledge of algorithm design principles
  • Basic proficiency in mathematical notation and proofs
NEXT STEPS
  • Study the concept of upper bounds in algorithm analysis
  • Explore various loss functions used in online learning
  • Learn about the implications of mistake bounds in online algorithms
  • Investigate advanced topics in algorithm design, such as competitive analysis
USEFUL FOR

This discussion is beneficial for students preparing for exams in computer science, particularly those focusing on algorithm design and online learning methodologies. It is also useful for educators and practitioners looking to deepen their understanding of loss functions and performance analysis in machine learning.

akerman
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Hello,

I am currently preparing myself for exams and I have a past exam question which I can't solve. This question concerns online learning and the following picture illustrates it: View attachment 5486
Is anyone able to help me out and propose a solution to this question?
 

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Hello, akerman! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
All I have right now is the initial setting where we do not have k classes but we just use {0,1}. For this setting I have that the mistakes or loss for S (online sequence of data) is:
$Loss(S) = \sum_{t=1}^{m} |y_{t} - \hat{y_{t}} |$

From there I don't know how to progress or solve this question...
 

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