2.12Communicate Worksheet

3 min read

This five-part digital activity consolidates the chapter’s communication concepts. You will match mechanisms to their applications, calculate the capacity of a discrete message and the effect of communication cost, then use an interactive graph to analyze how message loss changes task performance. The final prompt asks you to trade task success against bandwidth use. Every item except that short design judgment is automatically checkable.

What you will be able to do

• Match communication mechanisms and constraints to their roles in MARL. Understand
• Calculate message capacity and communication-adjusted rewards. Apply
• Interpret how communication reliability affects cooperative performance. Analyse
• Evaluate the trade-off between communication and task performance. Evaluate

1 · Match Mechanisms to Applications

Drag each block into a slot, or tap one and then tap a slot.

• Discrete message
• Continuous message
• Message loss
• Communication range
• Communication cost

1. An agent chooses one symbol from $\{0,1,2,3\}$.

   drop here

2. A message is received only by nearby agents.

   drop here

3. A sent message may never arrive.

   drop here

4. The reward is reduced whenever an agent sends information.

   drop here

5. An agent sends a learned real-valued vector.

   drop here

CheckClear

2 · Calculate Message Capacity

For a $b$-bit message, $|\mathcal{M}| = 2^b$.

2.1

A channel allows 3 bits per message. How many distinct messages can it represent?

Answerdistinct messagesCheck

2.2

You need at least 16 distinct messages. What is the minimum number of bits required?

AnswerbitsCheck

Need a hint?

2.3

A team needs to distinguish 8 situations but has only 2 bits. On average, how many situations must share each message?

Answersituations per messageCheck

Need a hint?

3 · Calculate Communication Cost

A cost term charges the team for talking: $r'_t = r_t - \lambda c_t$.

3.1

With $r_t = 10$, $\lambda = 0.5$ and $c_t = 4$, calculate $r'_t$.

AnswerCheck

3.2

Now raise the price to $\lambda = 1$, keeping $r_t = 10$ and $c_t = 4$.

AnswerCheck

3.3

At $\lambda = 1$, how many bits could the team afford before the four sent bits stop being worth it, if those bits raise $r_t$ from 7.5 to 10?

AnswerbitsCheck

Need a hint?

4 · Explore Message Loss and Performance

Measured on the Communication Lab task: four dishes, four symbols, two tabular learners, 20 seeds, 8000 evaluation trials each.

Message loss (%)

4.1

At what message-loss rate does success first fall below 0.80?

Answer% lossCheck

4.2

By how many percentage points does success fall between 0% and 40% loss?

Answerpercentage pointsCheck

5 · Evaluate a Communication Trade-off

Protocol A achieves 94% task success and sends 20 messages per episode.

Protocol B achieves 91% success and sends 6 messages per episode.

5.1

Which would you choose for a bandwidth-constrained robot system, and why?

AnswersReveal

1

Answer to 1.

Discrete message · communication range · message loss · communication cost · continuous message, matched to the descriptions in order.

2.1

Answer to 2.1.

$2^3 = 8$.

2.2

Answer to 2.2.

4 bits. $2^4 = 16$; three bits give only 8.

2.3

Answer to 2.3.

Two bits give 4 messages for 8 situations, so 2 situations share each message. The receiver disambiguates from context, and where it cannot, the team pays for the merge.

3.1

Answer to 3.1.

$10 - 0.5 \times 4 = 8$.

3.2

Answer to 3.2.

$10 - 1 \times 4 = 6$.

3.3

Answer to 3.3.

The messages bought $10 - 7.5 = 2.5$ of task reward, which at a price of 1 per bit pays for 2.5 bits. Sending 4 costs 4 and returns 2.5, so those messages lose the team 1.5 per step.

4.1

Answer to 4.1.

30%, where success is 0.773. At 20% it is still 0.849.

4.2

Answer to 4.2.

$1.000 - 0.695 = 0.305$, about 30.5 percentage points.

5.1

Answer to 5.1.

No single right answer.

B is the better default. It gives up 3 points of success and sends 70% fewer messages. Under a bandwidth constraint these are not comparable currencies: 3 points is a small bounded loss, while 20 messages per episode may simply not fit, making A’s 94% unavailable rather than expensive.

A is defensible if the channel carries it and the task is failure-sensitive.

A strong answer notes what the table omits: behaviour under message loss. A protocol sending 20 messages has redundancy; one sending 6 may need every one to arrive.

Review with Flashcards

Revisit the 10 key concepts, equations, and intuitions from this chapter.

Open Communicate Flashcards