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Changes to inactivity leak 

* Fixes parameters and makes clear that the inactivity leak is on a per-epoch basis (before the leak was technically 64 times too weak as it was calculated per-slot but applied per-epoch)
* Adds a `// 2` to the inactivity leak to compensate for it being applied twice
* Changes how it is calculated (no inactivity leak for not being part of the head, only basic leak)
* Separates out early inclusion incentives into a separate incentive component rather than being multiplicative with everything else
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vbuterin 2018-12-20 12:41:17 -05:00 committed by GitHub
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specs/core/0_beacon-chain.md
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@ -207,10 +207,10 @@ Unless otherwise indicated, code appearing in `this style` is to be interpreted
| `BASE_REWARD_QUOTIENT` | `2**10` (= 1,024) |
| `WHISTLEBLOWER_REWARD_QUOTIENT` | `2**9` (= 512) |
| `INCLUDER_REWARD_QUOTIENT` | `2**3` (= 8) |
| `INACTIVITY_PENALTY_QUOTIENT` | `2**34` (= 17,179,869,184) |
| `INACTIVITY_PENALTY_QUOTIENT` | `2**22` (= 4,194,304) |
* The `BASE_REWARD_QUOTIENT` parameter dictates the per-epoch reward. It corresponds to ~2.54% annual interest assuming 10 million participating ETH in every epoch.
* The `INACTIVITY_PENALTY_QUOTIENT` equals `INVERSE_SQRT_E_DROP_TIME**2` where `INVERSE_SQRT_E_DROP_TIME := 2**17 slots` (~9 days) is the time it takes the inactivity penalty to reduce the balance of non-participating [validators](#dfn-validator) to about `1/sqrt(e) ~= 60.6%`. Indeed, the balance retained by offline [validators](#dfn-validator) after `n` slots is about `(1-1/INACTIVITY_PENALTY_QUOTIENT)**(n**2/2)` so after `INVERSE_SQRT_E_DROP_TIME` slots it is roughly `(1-1/INACTIVITY_PENALTY_QUOTIENT)**(INACTIVITY_PENALTY_QUOTIENT/2) ~= 1/sqrt(e)`.
* The `INACTIVITY_PENALTY_QUOTIENT` equals `INVERSE_SQRT_E_DROP_TIME**2` where `INVERSE_SQRT_E_DROP_TIME := 2**11 epochs` (~9 days) is the time it takes the inactivity penalty to reduce the balance of non-participating [validators](#dfn-validator) to about `1/sqrt(e) ~= 60.6%`. Indeed, the balance retained by offline [validators](#dfn-validator) after `n` slots is about `(1-1/INACTIVITY_PENALTY_QUOTIENT)**(n**2/2)` so after `INVERSE_SQRT_E_DROP_TIME` slots it is roughly `(1-1/INACTIVITY_PENALTY_QUOTIENT)**(INACTIVITY_PENALTY_QUOTIENT/2) ~= 1/sqrt(e)`.
### Status codes
@ -1581,16 +1581,6 @@ For every `shard_committee` in `state.shard_committees_at_slots`:
* Let `total_balance(shard_committee) = sum([get_effective_balance(state, i) for i in shard_committee.committee])`.
* Let `inclusion_slot(state, index) = a.slot_included` for the attestation `a` where `index` is in `get_attestation_participants(state, a.data, a.participation_bitfield)`.
* Let `inclusion_distance(state, index) = a.slot_included - a.data.slot` where `a` is the above attestation.
* Let `adjust_for_inclusion_distance(magnitude, distance)` be the function below.
```python
def adjust_for_inclusion_distance(magnitude: int, distance: int) -> int:
"""
Adjusts the reward of an attestation based on how long it took to get included (the longer, the lower the reward).
Returns a value between ``0`` and ``magnitude``.
""
return magnitude // 2 + (magnitude // 2) * MIN_ATTESTATION_INCLUSION_DELAY // distance
```
### Receipt roots
@ -1606,7 +1596,6 @@ If `state.slot % POW_RECEIPT_ROOT_VOTING_PERIOD == 0`:
* Set `state.justification_bitfield |= 2` and `state.justified_slot = state.slot - 2 * EPOCH_LENGTH` if `3 * previous_epoch_boundary_attesting_balance >= 2 * total_balance`.
* Set `state.justification_bitfield |= 1` and `state.justified_slot = state.slot - 1 * EPOCH_LENGTH` if `3 * this_epoch_boundary_attesting_balance >= 2 * total_balance`.
### Finalization
Set `state.finalized_slot = state.previous_justified_slot` if any of the following are true:
@ -1625,33 +1614,36 @@ For every `shard_committee` in `state.shard_committees_at_slots`:
First, we define some additional helpers:
* Let `base_reward_quotient = BASE_REWARD_QUOTIENT * integer_squareroot(total_balance // GWEI_PER_ETH)`.
* Let `base_reward(state, index) = get_effective_balance(state, index) // base_reward_quotient // 4` for any validator with the given `index`.
* Let `inactivity_penalty(state, index, slots_since_finality) = base_reward(state, index) + get_effective_balance(state, index) * slots_since_finality // INACTIVITY_PENALTY_QUOTIENT` for any validator with the given `index`.
* Let `base_reward(state, index) = get_effective_balance(state, index) // base_reward_quotient // 5` for any validator with the given `index`.
* Let `inactivity_penalty(state, index, epochs_since_finality) = base_reward(state, index) + get_effective_balance(state, index) * epochs_since_finality // INACTIVITY_PENALTY_QUOTIENT // 2` for any validator with the given `index`.
#### Justification and finalization
Note: When applying penalties in the following balance recalculations implementers should make sure the `uint64` does not underflow.
* Let `slots_since_finality = state.slot - state.finalized_slot`.
* Let `epochs_since_finality = (state.slot - state.finalized_slot) // EPOCH_LENGTH`.
Case 1: `slots_since_finality <= 4 * EPOCH_LENGTH`:
Case 1: `epochs_since_finality <= 4`:
* Expected FFG source:
* Any [validator](#dfn-validator) `index` in `previous_epoch_justified_attester_indices` gains `adjust_for_inclusion_distance(base_reward(state, index) * previous_epoch_justified_attesting_balance // total_balance, inclusion_distance(state, index))`.
* Any [validator](#dfn-validator) `index` in `previous_epoch_justified_attester_indices` gains `base_reward(state, index) * previous_epoch_justified_attesting_balance // total_balance`.
* Any [active validator](#dfn-active-validator) `v` not in `previous_epoch_justified_attester_indices` loses `base_reward(state, index)`.
* Expected FFG target:
* Any [validator](#dfn-validator) `index` in `previous_epoch_boundary_attester_indices` gains `adjust_for_inclusion_distance(base_reward(state, index) * previous_epoch_boundary_attesting_balance // total_balance, inclusion_distance(state, index))`.
* Any [validator](#dfn-validator) `index` in `previous_epoch_boundary_attester_indices` gains `base_reward(state, index) * previous_epoch_boundary_attesting_balance // total_balance`.
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_boundary_attester_indices` loses `base_reward(state, index)`.
* Expected beacon chain head:
* Any [validator](#dfn-validator) `index` in `previous_epoch_head_attester_indices` gains `adjust_for_inclusion_distance(base_reward(state, index) * previous_epoch_head_attesting_balance // total_balance, inclusion_distance(state, index))`.
* Any [validator](#dfn-validator) `index` in `previous_epoch_head_attester_indices` gains `base_reward(state, index) * previous_epoch_head_attesting_balance // total_balance)`.
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_head_attester_indices` loses `base_reward(state, index)`.
* Inclusion distance:
* Any [validator](#dfn-validator) `index` in `previous_epoch_attester_indices` gains `base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // inclusion_distance(state, index)`
Case 2: `slots_since_finality > 4 * EPOCH_LENGTH`:
Case 2: `epochs_since_finality > 4`:
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_justified_attester_indices`, loses `inactivity_penalty(state, index, slots_since_finality)`.
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_boundary_attester_indices`, loses `inactivity_penalty(state, index, slots_since_finality)`.
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_head_attester_indices`, loses `inactivity_penalty(state, index, slots_since_finality)`.
* Any [validator](#dfn-validator) `index` with `status == EXITED_WITH_PENALTY`, loses `3 * inactivity_penalty(state, index, slots_since_finality)`.
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_justified_attester_indices`, loses `inactivity_penalty(state, index, epochs_since_finality)`.
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_boundary_attester_indices`, loses `inactivity_penalty(state, index, epochs_since_finality)`.
* Any [active validator](#dfn-active-validator) `index` not in `previous_epoch_head_attester_indices`, loses `base_reward(state, index)`.
* Any [validator](#dfn-validator) `index` with `status == EXITED_WITH_PENALTY`, loses `2 * inactivity_penalty(state, index, epochs_since_finality) + base_reward(state, index)`.
* Any [validator](#dfn-validator) `index` in `previous_epoch_attester_indices` loses `base_reward(state, index) - base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // inclusion_distance(state, index)`
#### Attestation inclusion
@ -1661,7 +1653,7 @@ For each `index` in `previous_epoch_attester_indices`, we determine the proposer
For every `shard_committee` in `state.shard_committees_at_slots[:EPOCH_LENGTH]` (i.e. the objects corresponding to the epoch before the current one), for each `index` in `shard_committee.committee`, adjust balances as follows:
* If `index in attesting_validators(shard_committee)`, `state.validator_balances[index] += adjust_for_inclusion_distance(base_reward(state, index) * total_attesting_balance(shard_committee) // total_balance(shard_committee)), inclusion_distance(state, index))`.
* If `index in attesting_validators(shard_committee)`, `state.validator_balances[index] += base_reward(state, index) * total_attesting_balance(shard_committee) // total_balance(shard_committee))`.
* If `index not in attesting_validators(shard_committee)`, `state.validator_balances[index] -= base_reward(state, index)`.
### Ejections
@ -1757,9 +1749,9 @@ Also perform the following updates:
If a validator registry update does _not_ happen do the following:
* Set `state.shard_committees_at_slots[:EPOCH_LENGTH] = state.shard_committees_at_slots[EPOCH_LENGTH:]`.
* Let `slots_since_finality = state.slot - state.validator_registry_latest_change_slot`.
* Let `epochs_since_finality = (state.slot - state.validator_registry_latest_change_slot) // EPOCH_LENGTH`.
* Let `start_shard = state.shard_committees_at_slots[0][0].shard`.
* If `slots_since_finality` is an exact power of 2, set `state.shard_committees_at_slots[EPOCH_LENGTH:] = get_new_shuffling(state.latest_randao_mixes[(state.slot - EPOCH_LENGTH) % LATEST_RANDAO_MIXES_LENGTH], state.validator_registry, start_shard)`. Note that `start_shard` is not changed from the last epoch.
* If `epochs_since_finality` is an exact power of 2, set `state.shard_committees_at_slots[EPOCH_LENGTH:] = get_new_shuffling(state.latest_randao_mixes[(state.slot - EPOCH_LENGTH) % LATEST_RANDAO_MIXES_LENGTH], state.validator_registry, start_shard)`. Note that `start_shard` is not changed from the last epoch.
### Proposer reshuffling