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CANITA Compressed Accelerated Gradient Method for Distributed Convex Optimization

Algorithms AIMech:CanitaCompressedAcceleratedGradientMethodForDistributedConvexOptimization DRAFT
Aliases: CANITA, Compressed Accelerated Gradient Method CANITA, CANITA Distributed Convex Optimization Algorithm
A compressed Nesterov-style accelerated gradient algorithm for distributed smooth convex optimization across n machines (Algorithm 1) that couples three momentum-coupled iterate sequences (x^t, y^t, z^t) with a randomized loopless control-variate reference point w^t (updated to z^t with probability p_t) and worker-side DIANA-style gradient shifts h_i^{t+1} = h_i^t + alpha_t Q_i^t(nabla f_i(w^t) - h_i^t) under randomized unbiased (omega)-compressors, achieving the accelerated O(sqrt((1 + omega) L / eps) + omega * (L / (n * eps))^{1/3} + (omega * L / (n * eps))^{1/2}) communication complexity in general smooth convex regimes without strong convexity.
Identity Notes & Concept Scope Distinct from non-accelerated DIANA (Mishchenko et al., 2019; O((1 + omega/n) L / eps) in general convex settings), ADIANA (Li et al., ICML 2020; requires strong convexity mu > 0), and uncompressed ANITA (Li, 2021). CANITA (Li & Richtarik, NeurIPS 2021, arXiv:2107.09461) is the first distributed method with communication compression to achieve the accelerated O(sqrt(L/eps)) leading term on general smooth convex objectives.

Claims & Grounded Evidence

4 Claims
Mechanism #canita-dual-compressed-difference-estimator-with-probabilistic-anchor-mechanism
At each communication round t, CANITA forms the extrapolated query point y^t = theta_t x^t + (1 - theta_t) w^t, each worker i transmits two compressed gradient differences Q_i^t(nabla f_i(y^t) - h_i^t) and Q_i^t(nabla f_i(w^t) - h_i^t) to form the global gradient estimator g^t = h^t + (1/n) sum_i Q_i^t(nabla f_i(y^t) - h_i^t) and shift update h_i^{t+1} = h_i^t + alpha_t Q_i^t(nabla f_i(w^t) - h_i^t), updates x^{t+1} = x^t - (eta_t/theta_t) g^t and z^t = theta_t x^{t+1} + (1 - theta_t) w^t, and resets w^{t+1} = z^t with probability p_t (or keeps w^t with probability 1 - p_t).
Scope #canita-accelerated-general-convex-communication-complexity-scope
Under L-average smoothness (Assumption 1) and unbiased omega-compression (Definition 1) with theta_t = 3(1+b)/(t + 9(1+b+omega)), p_t = 1/(1+b), alpha_t = 1/(1+omega), and b = min{omega, sqrt(omega(1+omega)^2 / n)} (Theorem 2 & Corollary 1), CANITA achieves an eps-suboptimal solution f(z^T) - f(x^*) <= eps in O(sqrt((1+omega) L / eps) + omega * (L / (n * eps))^{1/3} + (omega * L / (n * eps))^{1/2}) communication rounds, achieving strictly O(sqrt(L/eps)) round complexity when n >= omega^3.
Limitation #canita-unbiased-compressor-and-double-message-per-round-limitation
CANITA's convergence analysis requires randomized unbiased compression operators satisfying E[Q(x)] = x and E[||Q(x) - x||^2] <= omega ||x||^2 (excluding contractive biased compressors such as Top-k without error feedback) and transmits two compressed vectors per worker per round (for y^t and w^t).
Application #canita-distributed-convex-logistic-and-linear-regression-application
Applied to distributed regularized logistic regression and unregularized convex learning across multiple worker nodes using randomized sparsification (Rand-k) and quantization (QSGD).

⚠️ Curated Limitations & Negative Results

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes
AIO Target Class Mapping Relation Mapping Rationale
AIO:FederatedLearning
Federated Learning
 related_match CANITA is a communication-compressed accelerated distributed convex optimization algorithm applicable to multi-worker and federated training.

Evidence Sources & Primary Literature

3 Sources
Source ID Publication / Document Type / Access Reference & Checksum
r560-primary-pdf
Zhize Li, Peter Richtarik
primary paper
full_text
ID: https://api.openalex.org/works/https://doi.org/10.48550/arXiv.2107.09461
sha256:e0711a16e7e7…
r560-arxiv-abs
Zhize Li, Peter Richtarik
primary paper
abstract_only
ID: https://arxiv.org/abs/2107.09461
sha256:7d1dfa5d56b8…
r560-metadata-cr
Zhize Li, Peter Richtarik
primary paper
abstract_only
ID: https://api.openalex.org/works/https://doi.org/10.48550/arXiv.2107.09461
sha256:21114949f2e5…

Ontology & Grounding Topology

Open in interactive network graph →
CONCEPT KIND Algorithms AIMech:CanitaCompressedAcceleratedGradientMethodForDistributedConvexOptimization CANITA Compressed... 4 claims · 3 sources AIO GROUNDING AIO:FederatedLearning (1)

Curation Provenance

Curator: Antigravity
Method: ai_assisted
Model: Gemini
Created: 2026-10-19T10:43:00Z
Updated: 2026-10-19T10:43:00Z
Source File: data/curated/CanitaCompressedAcceleratedGradientMethodForDistributedConvexOptimization.yaml · Schema: curated_concept.yaml

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