Benchmarker Rewards

Benchmarker rewards are the rewards earned by Benchmarkers for performing proof-of-work on challenges in TIG.

TIG operates on an Optimizable Proof of Work (OPoW) concept in which benchmarkers are incentivized to balance different factors evenly during the PoW process. The total rewards distributed for proof-of-work done by benchmarkers is a fraction ${BM\%}$ of the total block reward:

Where $BM\%$ is the percentage of the block rewards that gets shared amongst all the Benchmarkers (before deducting the share with the delegators), which is currently set to 70%. This means that 70% of the block rewards are shared among all benchmarkers.

Each benchmarker $i$ receives $benchmarker\_reward_i$ from a block (before delegator deductions), where $benchmarker\_reward_i$ is calculated as:

The term $influence_i$ represents how much proof-of-work benchmarker $i$ has performed and how well they have balanced their factors.

There are two types of factors which are used to calculate the influence of a benchmarker.

• Challenge Factors
• Deposit factors

Factors are recalculated each block.

Challenge Factors

Challenge factors are derived from individual challenges. For each challenge $x$, benchmarker $i$ has an associated challenge factor calculated using their qualifying bundles:

Here, $num\_qualifiers_{i,x}$ is the number of qualifying bundles benchmarker $i$ has for challenge $x$ in the current block, and $total\_qualifiers_x=\sum_i num\_qualifiers_{i,x}$. If there are currently $n$ challenges, then each benchmarker has $n$ challenge factors — one for each challenge.

Qualifiers are determined using the Frontier mechanism.

Deposit Factors

Deposit factors are derived from TIG deposits. Each benchmarker $i$ has a ${self\_deposit\_factor}_i$ determined by their own deposit and a ${delegated\_deposit\_factor}_i$ determined by deposits delegated to them. These are calculated as follows:

Note that $\langle{challenge\_factor}_i\rangle$ is the average of the challenge factors and measures how actively a benchmarker is participating in the current block. The $\min$ function caps a benchmarker’s deposit factor based on their challenge performance.

Here ${self\_deposit}_i$ is the amount of TIG that benchmarker $i$ has deposited, ${delegated\_deposit}_i$ is the amount of TIG delegated to benchmarker $i$ through the delegated deposit mechanism, and ${total\_deposit}$ and ${total\_delegated\_deposit}$ are the total deposits and delegated deposits of all benchmarkers whose cutoff is non-zero.

Influence

To calculate the influence of a benchmarker $i$, the following steps are performed:

1. Collect the set of factors for benchmarker $i$ : $\{f_j ~:~ f_j ~\text{is a factor for benchmarker }i\}$. Let $\hat f_i$ be the vector of these factors.
2. Compute weights $w_j$, and attribute each factor $f_j$ with a weight $w_j$. The weights are normalised. The weights are the same for all benchmarkers.
3. Compute the weighted mean $\langle \hat f_i \rangle$ and variance $\sigma^2_i$ of the factors of benchmarker $i$. Set $\mathcal{S}_i=\frac{\sigma_i^2}{\langle \hat f_i \rangle (1-\langle \hat f_i \rangle )}$.
4. We then set the influence of benchmarker $i$ to be:

Note: In the above formula:

• $k$ is a constant currently set to $1.5$.
• The exponential term is bounded in $[0,1]$.
• As $\mathcal{S}_i$ increases, the benchmarker is penalized for their imbalance, no variation means the exponential term takes the value $1$ and the benchmarker is not penalized.
• The term $\mathcal{S}_i$ is bounded in $[0,1]$. For a fixed $\langle \hat f_i \rangle$ the maximum of $\sigma_i^2$ is $\langle \hat f_i \rangle(1-\langle \hat f_i \rangle)$, hence $\mathcal{S}_i$ measures the spread of the data relative to its mean.
• Weighting lets us:
  • Onboard new challenges smoothly.
  • Weight Deposit Factors differently from Challenge Factors.