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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.

  • Loss minimisation (constant model)
  • Russian original · English translation

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.

Read the task statement in English 225 words

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 cc (a constant model). You are given a set of true values:

y={1,2,3,9,10,10}.y = \{1, 2, 3, 9, 10, 10\}.

Consider two quality functions: L1(c)=iyicL_1(c) = \sum_i |y_i - c| and L2(c)=i(yic)2L_2(c) = \sum_i (y_i - c)^2.

a) Find the value c1c_1 that minimises L1(c)L_1(c). If there are several optimal values, give the smallest of them as your answer.

b) Find the value c2c_2 that minimises L2(c)L_2(c). 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.

Details

Year
2026, Moscow, Russia (in person)
Round
Municipal Stage (Moscow), grades 9–11 · Task 3
Language
Russian; English translation by SOTA
License
Not stated by the source