---
kind: concept
slug: client-selection
title: Client selection in federated learning
summary: >-
  Choosing which devices join each federated round. Each client gets a statistical utility (likely usefulness of its update) times a system utility (speed), and the top scorers are picked. Variants differ in the usefulness signal (data size, loss, model divergence, gradient norm) and in how stragglers are handled (hard or soft deadline). One source, a survey with no experiments.
tags: [federated-learning, client-selection, survey, heterogeneity, scheduling]
papers: ["2211.01549"]
related: [federated-learning, federated-aggregation, personalized-federated-learning, clustered-federated-learning, multi-armed-bandit]
status: draft
updated_at: 2026-11-03
---

## Overview

In cross-device federated learning, the server cannot use every client in every
round. Clients differ in hardware, network speed, availability and data, and
random selection ignores all of this [arxiv:2211.01549 §1, §3]. The problem is
to decide, each round, which clients to ask for an update.

The shared idea is to score each client and take the highest scores. The
overall score is a statistical utility (usefulness of the client's update)
multiplied by a system utility (speed) [arxiv:2211.01549 §4, eq. 1]. A
client's usefulness is usually only known after it has trained, so methods
forecast it beforehand and correct the forecast once the client has joined a
round [arxiv:2211.01549 §4.3]. The survey that this page draws on is
[Client Selection in Federated Learning: Principles, Challenges, and Opportunities](/papers/2211.01549).
It is a survey with no experiments of its own, so the page describes the design
space and does not rank the methods.

## Variants

### Statistical utility from data samples

The score uses facts about the client's local samples [arxiv:2211.01549 §4.1.1]:

- **Client data size.** The number of samples is a valid proxy when samples
  are about equally informative, for example under IID data [arxiv:2211.01549
  eq. 2].
- **Exact importance-sampling optimum.** Scores each sample by the squared norm
  of its gradient. The survey calls this the best solution in principle but
  very costly to compute [arxiv:2211.01549 eq. 3, §4.1.1].
- **Loss-based approximation.** Uses the sample count times the root mean square
  of the per-sample losses, attributed to Oort on the reasoning that a large loss
  tends to mean a large gradient. The survey states this as a cited reasoning,
  not a derivation [arxiv:2211.01549 eq. 4, §4.1.1]. Card: [Client Selection in
  Federated Learning](/papers/2211.01549).
- **Cumulative loss.** Used by POWER-OF-CHOICE [arxiv:2211.01549 eq. 5].

### Statistical utility from the model

These measures compare the client's model or update with the global model
[arxiv:2211.01549 §4.1.2]:

- normalized divergence of the weights [arxiv:2211.01549 eq. 6];
- sign agreement, the share of weights whose sign matches the global model
  [arxiv:2211.01549 eq. 7];
- a layer-wise cosine of weight movement, from FCFL [arxiv:2211.01549 eq. 8];
- the norm of the weight change during local training [arxiv:2211.01549 eq. 9];
- the L2 norm of the local gradients [arxiv:2211.01549 eq. 10];
- the inner product of local and global gradients. FOLB and FedPNS drop clients
  whose product is negative [arxiv:2211.01549 eq. 11].

### System utility: hard or soft deadline

- **Hard deadline.** A client scores only if its round time is below a deadline
  T. The indicator is 1 for clients inside T and 0 otherwise [arxiv:2211.01549
  eq. 12]. The round time covers local training, transmission and compression
  [arxiv:2211.01549 §4.2].
- **Soft deadline (Oort).** Stragglers are scaled down rather than removed. The
  factor is (T / t_i) raised to a power alpha, and equals 1 inside the deadline
  [arxiv:2211.01549 eq. 13]. The survey does not state a value for alpha.
- **Other measures.** The deadline can measure FLOPs or bandwidth instead of
  time. FedBalancer adjusts T automatically [arxiv:2211.01549 §4.2].

### Combining the terms

- **Multiplicative** (eq. 1). The survey says other factors, such as fairness,
  robustness or privacy, fit the same form, and that a term can be ignored by
  setting it to 1 [arxiv:2211.01549 §4.4].
- **Additive, weighted.** Eiffel sums its terms with weights instead
  [arxiv:2211.01549 §4.4].

## When to use which

Choices are based on the constraints the survey discusses. The survey reports
no experiments comparing these choices, so none of the rows below is a measured
ranking.

| Situation | Use | Why |
|---|---|---|
| Client data is roughly equally informative, and scoring must be cheap | Data size, eq. 2 | The survey gives this as valid under equal informativeness [arxiv:2211.01549 §4.1.1] |
| Per-sample difficulty should matter, and exact gradient scores are too costly | Loss-based approximation, eq. 4 | The survey names it as the practical stand-in for the exact optimum [arxiv:2211.01549 §4.1.1] |
| The server can wait for clients to train before choosing them | Model-based measures, eqs. 6–11 | These need the client's trained model or update [arxiv:2211.01549 §4.1.2] |
| Round time must stay under a fixed budget | Hard deadline, eq. 12 | Clients over the deadline are excluded [arxiv:2211.01549 §4.2] |
| Slow clients should still count, but less | Soft deadline, eq. 13 | Stragglers are scaled, not removed. Tune alpha, which the survey leaves open [arxiv:2211.01549 §4.2] |
| Bandwidth or energy is the bottleneck | Wireless-aware methods, e.g. OCEAN and the block-fading method | Survey table lists them as system-targeted [arxiv:2211.01549 tab. 1] |
| Devices are only sometimes available | Availability-dependent selection, e.g. F3AST | The survey lists it as the availability-aware entry [arxiv:2211.01549 tab. 1], and availability is an open challenge [arxiv:2211.01549 §6] |
| Exploration of unseen clients is needed alongside exploitation | Oort-style exploration and exploitation | Named as part of Oort's design [arxiv:2211.01549 tab. 1]. The trade-off has no settled rule [arxiv:2211.01549 §6] |
| Extra goals such as fairness or robustness must be added | Multiplicative term, eq. 1, or additive weights | Both forms are discussed. No comparison is reported [arxiv:2211.01549 §4.4] |

Methods that are hierarchical, serverless, reinforcement-learning based or
fuzzy-logic based are outside the survey's scope [arxiv:2211.01549 §2.2, §8].
Do not apply the rules above to them without checking their own sources.

## Implementation sketch

A round-level sketch that follows the survey's structure: compute each client's
utility, then keep the top M. Stat and sys are the choices above; the survey
does not fix how M interacts with exploration [arxiv:2211.01549 §4.3, §6].

```pseudocode
# Score every client for this round  [arxiv:2211.01549 eq. 1]
# Input:  clients, number to pick M, deadline T [arxiv:2211.01549 §4.2]
# Output: ids of the M selected clients

def pick_clients(clients, M, T):
    scores = {}
    for c in clients:
        # Use the measured value if the client has trained, else a forecast
        # [arxiv:2211.01549 §4.3]
        stat = statistical_term(c)
        # Speed term: soft or hard deadline  [arxiv:2211.01549 eq. 12, eq. 13]
        sys = speed_term(c, T)
        scores[c.id] = stat * sys
    # Highest scores join the round  [arxiv:2211.01549 §4.3]
    return top_m_ids(scores, M)
```

```pseudocode
# Soft-deadline speed term (Oort style)  [arxiv:2211.01549 eq. 13]
# Input:  t_i round time, T deadline, alpha penalty exponent (not stated)
# Output: factor in (0, 1]

def speed_term(t_i, T, alpha):
    # Stragglers are scaled down, not removed  [arxiv:2211.01549 §4.2]
    if t_i <= T:
        return 1.0
    return (T / t_i) ** alpha
```

## Contradictions

- **Divergence direction.** Some work prefers clients whose models diverge most
  from the global model, and other work shows the opposite [arxiv:2211.01549
  §7.2]. For sign agreement, the cited study favours the lower value
  [arxiv:2211.01549 §4.1.2]. The survey does not resolve this.
- **Deadline boundary.** Eq. 12 keeps clients with t_i strictly below T, while
  the text describes removing clients whose time is longer than T. Eq. 13 gives
  1 at t_i = T. The text and the two equations disagree at the boundary
  [arxiv:2211.01549 §4.2, eq. 12, eq. 13].
- **Quoted figures.** The heterogeneity figures (accuracy drop up to 9.2%,
  convergence time 2.64X longer) come from one cited smartphone study and were
  not verified by the survey [arxiv:2211.01549 §3]. Gboard's 100 clients per
  round and about 2-minute deadline are one project's values, not general
  settings [arxiv:2211.01549 §4.2, §7.1].

## Papers

- [Client Selection in Federated Learning: Principles, Challenges, and Opportunities](/papers/2211.01549): survey of utility-based client selection, its formulas, 15 representative methods and open problems. No experiments of its own.