Pith Number

pith:K7DK3EPK

pith:2026:K7DK3EPKEU7T4AWJ3RO5UZJG7D

not attested not anchored not stored refs pending

Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning

Harin Lee, Min-hwan Oh

A simple algorithm with tunable exploration bonuses yields distributional regret bounds for multi-armed bandits and episodic reinforcement learning.

arxiv:2605.05102 v3 · 2026-05-06 · cs.LG · stat.ML

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\pithnumber{K7DK3EPKEU7T4AWJ3RO5UZJG7D}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

As a special case, for multi-armed bandits with A arms and horizon T, we obtain a distributional regret bound of order O(√(AT log(1/δ))), confirming the conjecture of Lattimore & Szepesvári (2020, Section 17.1) for the first time.

C2weakest assumption

The derivation assumes that the exploration bonus parameters can be chosen arbitrarily while still yielding the stated bounds, and relies on the standard stochastic assumptions for rewards and transitions without specifying potential violations or edge cases.

C3one line summary

Presents a UCBVI-style algorithm achieving optimal distributional regret bounds O(sqrt(AT log(1/δ))) in multi-armed bandits, confirming a 2020 conjecture.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-23T01:13:05.443871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57c6ad91ea253f3e02c9dc5dda6526f8ea6ceab9e1bb0f5bd987335be5e419f3

Aliases

arxiv: 2605.05102 · arxiv_version: 2605.05102v3 · doi: 10.48550/arxiv.2605.05102 · pith_short_12: K7DK3EPKEU7T · pith_short_16: K7DK3EPKEU7T4AWJ · pith_short_8: K7DK3EPK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/K7DK3EPKEU7T4AWJ3RO5UZJG7D \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 57c6ad91ea253f3e02c9dc5dda6526f8ea6ceab9e1bb0f5bd987335be5e419f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb4e4db1b648018d451418e33b7ec4fc73a9d128389207f70fab1779c6f0e4f3",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-06T16:38:30Z",
    "title_canon_sha256": "40eecbc0876d460c72284218363e9d6bb5ee69f1a5e5182b860ec739b153c06e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.05102",
    "kind": "arxiv",
    "version": 3
  }
}