Adaptive parallel tempering
Algorithms AIMech:AdaptiveParallelTempering DRAFT
Aliases: Adaptive parallel tempering algorithm
A parallel-tempering algorithm that adapts temperature gaps and within-replica random-walk proposal parameters through projected stochastic approximation.
Identity Notes & Concept Scope
This record is the fixed-replica-count Miasojedow–Moulines–Vihola 2012 construction. Its multiplicative inverse-temperature parameterization and all-pair swap-probability updates differ from later author software using increments of reciprocal temperatures and updates for selected pairs. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 181 prior native IDs/names/aliases. Ignored-inclusive searches of both full checkouts found prior discovery leads, neighboring sampler discussions and unrelated author-name/environment substrings. Existing random-walk Metropolis, delayed-rejection, fixed symmetric delayed-rejection and RAM records were inspected; shared components do not make these procedures equivalent.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
With fixed L≥2, alpha_star in (0,1) and epsilon in (0,1), set beta1=1 and beta_(l+1)=beta_l exp(−exp(rho_l)). Initialize within the parameter constraint sets and positive target support. At each iteration use the previous temperatures and proposal covariances for an adjacent exchange followed by local Gaussian Metropolis moves. From the retained post-propagation population X_new, compute every adjacent hypothetical exchange probability h_l=min(1,[pi(X_(l+1))/pi(X_l)]^(beta_l−beta_(l+1))). Update each rho_l by projection of rho_l+gamma1_n(h_l−alpha_star) onto a fixed finite interval. For each replica update mu_l=(1−gamma2_n)mu_l+gamma2_n X_new,l, and project (1−gamma2_n)Gamma_l+gamma2_n(X_new,l−mu_old,l)(X_new,l−mu_old,l)^T onto matrices with eigenvalues in [epsilon,epsilon^−1]. Update T_l by interval projection of T_l+gamma3_n(alpha_local,l−alpha_star), where alpha_local is that iteration’s local proposal acceptance probability. Use Sigma_l=exp(T_l)Gamma_l for later Gaussian proposals. Thus T is log variance, not log standard deviation; all adaptation follows the completed transition.
⚠️ Curated Limitations & Negative Results
- The record uses projected covariance and log-scale adaptation with separate step sequences; the mean recursion itself is not projected. Finite rho bounds keep ordered positive inverse temperatures, and the replica count is fixed.
- Every rho update uses a hypothetical adjacent swap probability at the post-propagation state, not just the pair actually selected or a binary swap outcome.
- The strong-law and temperature-convergence results have different hypotheses. Temperature convergence additionally needs stronger step conditions and the target solution inside the projection bounds; projection alone does not guarantee the desired rate is attainable.
- The continuous-target results assume the stated tail/contour, moment and step-size conditions. Experiments omitting projections do not prove unrestricted adaptive validity.
- The optional RAM proposal variant in Section 2.3 uses a physical increment where the original RAM paper uses a standardized proposal direction. That variant is excluded here; the covariance-based construction is the inspected core.
- No changing-replica-count method, unrestricted adaptive convergence, universal efficiency claim or benchmark reproduction is asserted.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | This procedure adapts a family of Markov transition kernels that are target-invariant at frozen settings. Its sampled-state history is not assumed to be a homogeneous Markov chain, and adaptive validity requires separate assumptions. AIO MarkovChain is a process/model beneath Network; this is a related method-to-process mapping, not equivalence, an is-a assertion or a convergence guarantee. The frozen joint population target depends on the ladder; the cold marginal remains pi. This does not assert one invariant joint law throughout adaptation. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Błażej Miasojedow, Eric Moulines, Matti Vihola
|
primary paper
full_text
|
ID: arXiv:1205.1076v1
sha256:4c0f3ba8a5a8…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T07:40:20Z
Updated: 2026-10-11T07:41:38Z
Source File:
data/curated/AdaptiveParallelTempering.yaml