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Subspace Parameter Selection Report

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the original version of this document on HackMD

Fig: Speed run over the PSuU workflow analysis notebook Screen Recording 2024-04-24 at 23.05.38

Intro

Summary Following the economic design initiative to propose the Subspace Issuance Function, this parameter selection initiative will involve a computational science workflow to support the parameter selection decision-making process for the subspace economic system.

In this document, we will

  • describe the simulation that generated our data,
  • interpret the simulation output in terms of correlation & confidence,
  • and provide parameter recommendations.

Project Goal Determine the "best" initial parameter ranges for the newly designed issuance function, as well as other key system parameters, at launch of the Subspace protocol.

Simulation Details

The simulations were prepared and interpreted as per the Subspace PSuU Methodology document. The model and notebooks used by the analysis can be found on the BlockScience/subspace GitHub repository, tagged as recommendations-v1. In particular, we've used the exploratory/inspect_psuu_timestep_tensor notebook for inspecting individual runs and the workflows/psuu.ipynb notebook for interprating the aggregated data.

The data (timestep and trajectory tensors) can be found on an Amazon S3 bucket located at https://subspace-simulations.s3.us-east-2.amazonaws.com.

Characteristics of the Resulting Dataset (or Timestep Tensor)

  • Temporal Coverage: Daily Measurements over 3 years (1,096 state measurements per simulation trajectory)
  • Count of Controllable Parameter Combinations: 5,832
  • Count of Environmental Parameter Combinations: 12
  • Count of Total Parameter Combinations: 69,984
  • Monte Carlo Runs: 3
  • Count of Simulation Trajectories: 209,952
  • Count of State Measurements: 230,108,392

Controllable Parameters values swept

Controllable Parameter Values
component_1_initial_period_start {0, 14 days, 30 days}
component_1_max_reference_subsidy {1SSC/blk, 4SSC/blk, 7SSC/blk}
component_1_max_cumulative_subsidy {10%, 30% and 50%}
component_2_initial_period_start {0, 14 days, 30 days}
component_2_initial_period_duration {6mo, 1yr, 2yr, 4yr}
component_2_max_reference_subsidy {1SSC/blk, 4SSC/blk, 7SSC/blk}
component_2_max_cumulative_subsidy {10%, 30% and 50%}
reward_proposer_share {10%, 33%}
weight_to_fee {1, 100, 1,000, 10,000}

Simulation Interpretation

In this section we provide correlation & confidence interpretations for

  1. each parameter relative to a single KPI label (e.g. 0 or 1) and
  2. each parameter relative to a System Goal individually (e.g. aggregation of KPIs)

KPI legend

  • KPI 1: mean_relative_community_owned_supply
  • KPI 2: mean_farmer_subsidy_factor
  • KPI 3: mean_proposing_rewards_per_newly_pledged_space
  • KPI 4: mean_proposer_reward_minus_voter_reward
  • KPI 5: cumm_rewards_before_1yr
  • KPI 6: abs_sum_storage_fees_per_sum_compute_fees
  • KPI 7: cumm_rewards

System Goal legend

  • Goal 1: Rational Economic Incentives
  • Goal 2: Community Incentivization
  • Goal 3: Supply and Demand Equilibrium / Distributional Equilibrium

Interpretation legend Relationship of Parameter to KPI label (i.e. for positive, larger values of parameter leads to more KPI = true outcomes)

  • +: Positive correlation against the KPI label (eg. larger parameter values reinforces the intent)
  • -: Negative correlation against the KPI label (eg. smaller parameter values reinforces the intent)
  • o: Uncorrelated against the KPI label
  • ?: Inconclusive

Confidence and/or Effect Strength

  • C: Conclusive and/or Large Importance
  • I: Indicative and/or Minor Importance
  • ?: Inconclusive and/or Un-important

Interpretation #1: each parameter relative to a single KPI label (e.g. 0 or 1)

Parameter / KPI 1 2 3 4 5 6 7
component_1_initial_period_start -,C ? ? ? -,I ? -,I
component_1_max_reference_subsidy +,C -,C +,C +,C +,C ? +,C
component_1_max_cumulative_subsidy o, I ? ? ? ? ? ?
component_2_initial_period_start -,C ? ? ? -,I ? -,I
component_2_initial_period_duration ? ? ? ? ? ? ?
component_2_max_reference_subsidy +,C -,C +,C +,C +,C ? +,C
component_2_max_cumulative_subsidy ? ? ? ? +,C ? ?
reward_proposer_share o,C o,C ? ? o,C ? o,C
weight_to_fee o,C ? o,C o,C o,C ? o,C

Interpretation #2: each parameter relative to a System Goal individually (e.g. aggregation of KPIs)

System Goal <> KPI mapping

  • Goal 1 <> KPI 3, 4
  • Goal 2 <> KPI 1, 5
  • Goal 3 <> KPI 2, 6, 7

Note: each KPI weighted equally in aggregation

Parameter Goal 1 Goal 2 Goal 3 Combined
component_1_initial_period_start -,I ? +,I -C
component_1_max_reference_subsidy +,C +,C -,C +,C
component_1_max_cumulative_subsidy ? ? ? ?
component_2_initial_period_start -,I -,I ? -C
component_2_initial_period_duration +,? ? ? ?
component_2_max_reference_subsidy +,C +,C -,C +,C
component_2_max_cumulative_subsidy +,I ? ? ?
reward_proposer_share ? ? ? ?
weight_to_fee o,C o,C ? ?

Parameter Recommendations

In this section we provide 3 sets of parameter recommendations based on the simulation output data, and correlation evaluation from above.

  1. Global Point number - A single value for each parameter, assuming all system goals equally weighted, and following the decision-making heuristic:

    • Positive correlation -> pick highest sweep value
    • Negative correlation -> pick lowest sweep value
    • Uncorrelated or inconclusive -> pick mid-point of sweep values
    • Average selected values
    Parameter Value
    component_1_initial_period_start 0 days
    component_1_max_reference_subsidy 7.0 SSC/blk
    component_1_max_cumulative_subsidy 30% of MaxIssuance
    component_2_initial_period_start 0 days
    component_2_initial_period_duration 1.5 years
    component_2_max_reference_subsidy 7.0 SSC/blocks
    component_2_max_cumulative_subsidy 30% of MaxIssuance
    reward_proposer_share 20%
    weight_to_fee 500 Shannon

  2. Local Range for Single Goal Optimization - A range of values for each parameter that optimize for a single goal, following the decision-making heuristic:

    • Positive correlation -> select top two sweep values (use mid-point if only two values swept)
    • Negative correlation -> select bottom two sweep values (use mid-point if only two values swept)
    • Uncorrelated or inconclusive -> full range of sweep values
    Parameter Max Goal 1 Max Goal 2 Max Goal 3
    component_1_initial_period_start 0 days 14 days 30 days
    component_1_max_reference_subsidy 7.0 SSC/blk 7.0 SSC/blk 1.0 SSC/blk
    component_1_max_cumulative_subsidy 30% of MaxIssuance 30% of MaxIssuance 30% of MaxIssuance
    component_2_initial_period_start 0 days 0 days 14 days
    component_2_initial_period_duration 1.5 years 1.5 years 1.5 years
    component_2_max_reference_subsidy 7.0 SSC/blk 7.0 SSC/blk 1.0 SSC/blk
    component_2_max_cumulative_subsidy 30% of MaxIssuance 30% of MaxIssuance 30% of MaxIssuance
    reward_proposer_share 20% 20% 20%
    weight_to_fee 500 Shannon 500 Shannon 500 Shannon

  3. Global Range - A range of values, assuming equally weighted system goals, and following the decision-making heuristic:

    • Positive correlation -> select top two sweep values (use mid-point if only two values swept)
    • Negative correlation -> select bottom two sweep values (use mid-point if only two values swept)
    • Uncorrelated or inconclusive -> full range of sweep values
    • Average both range values
    Parameter Global Range
    component_1_initial_period_start Between 0 and 7 days
    component_1_max_reference_subsidy Between 5.5 and 7.0 SSC/blk
    component_1_max_cumulative_subsidy Between 10% and 50% MaxIssuance
    component_2_initial_period_start Between 0 and 7 days
    component_2_initial_period_duration Between 6mo and 4 years
    component_2_max_reference_subsidy Between 5.5 and 7.0 SSC/blk
    component_2_max_cumulative_subsidy Between 10% and 50% MaxIssuance
    reward_proposer_share Between 10% and 33%
    weight_to_fee Between 1 and 10,000 Shannon