Checklist VsOSh AI 2026 Municipal Stage (Moscow), grades 9–11 · Task 3
Minimising L1 and L2
Russian title: Минимизация L1 и L2
Find the constant predictions that minimise the absolute and squared losses on a small sample.
The task
A constant regression model always predicts the same number c. For the true values y = {1, 2, 3, 9, 10, 10}, consider L₁(c) = Σ|y_i − c| and L₂(c) = Σ(y_i − c)².
(a) Find c₁ minimising L₁(c) (the smallest one if there are several). (b) Find c₂ minimising L₂(c) (the smallest one if there are several).
Abridged and translated by SOTA from the official Russian materials. The official statement has the exact rules, and it wins wherever this summary differs.
In English
This task was published in Russian. SOTA translated its 4 files into English on 16 September 2026.
- Task statement Russian original of Task statement
- Official solution Russian original of Official solution
- Full paper (all tasks of the stage) Russian original of Full paper (all tasks of the stage)
- All answers and solutions of the stage Russian original of All answers and solutions of the stage
Read the task statement in English
Minimising L1 and L2
English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].
Task 3 of the municipal stage (Moscow) of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence, grades 9–11 (variant III). Original: tasks-ai-9-11-mun-msk-25-26.pdf.
You are tuning the simplest possible regression model, which always predicts the same number (a constant model). You are given a set of true values:
Consider two quality functions: and .
a) Find the value that minimises . If there are several optimal values, give the smallest of them as your answer.
b) Find the value that minimises . If there are several optimal values, give the smallest of them as your answer.
Translator's note: this task's points are not stated in the statement paper (whose total is 600 points); the official answers give a maximum of 100 points, 50 for each part (exact match of the answer).
Translated by SOTA. The Russian original is the official version and wins wherever the two differ. Translated from the statement and answer PDFs of the Moscow municipal stage (grades 9–11) on vos.olimpiada.ru. The statement paper gives no per-task points; the 100 points (50 per part) come from the official answers. If you organise this olympiad and would like the translation removed, email [email protected] and we will take it down.
At a glance
- You get
- Statement only.
- You submit
- Two numbers (c₁ and c₂).
- Scoring
- Exact answer; the per-task maximum is not stated for this task in the statement file (the paper totals 600 points).
- Format
- Municipal stage (Moscow), 17 December 2025, grades 9–11; individual; 180 minutes; answers and programs submitted to an online testing system; maximum 600 points for the paper.