User Dynamics in Machine Learning Systems

Sarah Dean, Cornell CS

Networks & Cognition Workshop, June 2023

Our digital world is increasingly algorithmically mediated

Motivation

and these algorithms are powered by machine learning

\(\to\)

historical movie ratings

new movie rating

Machine Learning Systems

from actions impacting the world

Dynamics arise

from data impacting the policy

Machine Learning Systems

  1. Preference Dynamics
  2. Implications: Personalization & Harm
  3. Retention Dynamics

Outline

How do we design reliable algorithms that account for user dynamics?

Setting: Preference Dynamics

\(a_t\)

               \(y_t\)

Interests may be impacted by recommended content

preference state \(s_t\)

expressed preferences

recommended content

recommender policy

Setting: Preference Dynamics

\(a_t\)

\(y_t = \langle s_t, a_t\rangle + w_t  \)

Interests may be impacted by recommended content

expressed preferences

recommended content

recommender policy

\(\approx\)

\(y_{ui} \approx s_u^\top a_i\)

underlies factorization-based methods

preference state \(s_t\)

Setting: Preference Dynamics

\(a_t\)

\(y_t = \langle s_t, a_t\rangle + w_t  \)

Interests may be impacted by recommended content

expressed preferences

recommended content

recommender policy

underlies factorization-based methods

state \(s_t\) updates to \(s_{t+1}\)

Preference Dynamics

items \(a_t\in\mathcal A\subseteq \mathcal S^{d-1}\)

\(y_t = \langle s_t, a_t\rangle + w_t  \)

\(s_{t+1} = f_t(s_t, a_t)\)

preferences \(s\in\mathcal S^{d-1}\)

Preference Dynamics

items \(a_t\in\mathcal A\subseteq \mathcal S^{d-1}\)

\(y_t = \langle s_t, a_t\rangle + w_t  \)

\(s_{t+1} \propto s_t + \eta_t a_t\)

preferences \(s\in\mathcal S^{d-1}\)

Assimilation: interests may become more similar to recommended content

initial preference
resulting preference

Preference Dynamics

items \(a_t\in\mathcal A\subseteq \mathcal S^{d-1}\)

\(y_t = \langle s_t, a_t\rangle + w_t  \)

Biased Assimilation: interest update is proportional to affinity

\(s_{t+1} \propto s_t + \eta_t\langle s_t, a_t\rangle a_t\)

preferences \(s\in\mathcal S^{d-1}\)

Proposed by Hązła et al. (2019) as model of opinion dynamics

initial preference
resulting preference

Prior Work

2. Biased assimilation

\(s_{t+1} \propto s_t + \eta_t\langle s_t, a_t\rangle a_t\)

When recommendations are made globally, the outcomes differ:

initial preference
resulting preference

1. Assimilation

\(s_{t+1} \propto s_t + \eta_t a_t\)

polarization (Hązła et al. 2019; Gaitonde et al. 2021)

homogenized preferences

Personalized Recommendations

Regardless of whether assimilation is biased,

Personalized fixed recommendation \(a_t=a\)

$$ s_t = \alpha_t s_0 +  \beta_t a$$

positive and decreasing

increasing magnitude (same sign as \(\langle s_0, a\rangle\) if biased assimilation)

\(s_{t+1} \propto s_t + \eta_t\langle s_t, a_t\rangle a_t\)

\(s_{t+1} \propto s_t + \eta_t a_t\)

Personalized Recommendations

Regardless of whether assimilation is biased,

\(s_{t+1} \propto s_t + \eta_t\langle s_t, a_t\rangle a_t\)

\(s_{t+1} \propto s_t + \eta_t a_t\)

Implications [DM22]

  1. It is not necessary to identify preferences to make high affinity recommendations

Personalized Recommendations

Regardless of whether assimilation is biased,

\(s_{t+1} \propto s_t + \eta_t\langle s_t, a_t\rangle a_t\)

\(s_{t+1} \propto s_t + \eta_t a_t\)

initial preference
resulting preference

Implications [DM22]

  1. It is not necessary to identify preferences to make high affinity recommendations

  2. Preferences "collapse" towards whatever users are often recommended

Personalized Recommendations

Regardless of whether assimilation is biased,

\(s_{t+1} \propto s_t + \eta_t\langle s_t, a_t\rangle a_t\)

\(s_{t+1} \propto s_t + \eta_t a_t\)

initial preference
resulting preference

Implications [DM22]

  1. It is not necessary to identify preferences to make high affinity recommendations

  2. Preferences "collapse" towards whatever users are often recommended

  3. Non-manipulation (and other goals) can be achieved through randomization

Harmful Recommendations

Simple choice model: given a recommendation, a user

  1. Selects the recommendation with probability determined by affinity
  2. Otherwise, selects from among all content based on affinities

Preference dynamics lead to a new perspective on harm

Simple definition: harm caused by consumption of harmful content

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\(\mathbb P\{\mathrm{click}\}\)

Harmful Recommendations

Due to preference dynamics, there may be downstream harm, even when no harmful content is recommended

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Recommendation: ♫

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Recommendation: 𝅘𝅥𝅯

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Harmful Recommendations

Due to preference dynamics, there may be downstream harm, even when no harmful content is recommended

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𝅗𝅥

𝅘𝅥𝅯

𝅗𝅥

Recommendation: ♫

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Recommendation: 𝅘𝅥𝅯

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\(\mathbb P\{\mathrm{click}\}\)

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Harmful Recommendations

Due to preference dynamics, there may be downstream harm, even when no harmful content is recommended

Recommendation: ♫

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Recommendation: 𝅘𝅥𝅯

This motivates a new recommendation objective which takes into account the probability of future harm [CDEIKW23]

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\(\mathbb P\{\mathrm{click}\}\)

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User Choice & Retention

Even if individual preferences are immutable, population level effects may be observed due to retention dynamics

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The dynamic of retention & specialization can lead to representation disparity (Hashimoto et al.) and segmentation [DCRMF23]

User Choice & Retention

Even if individual preferences are immutable, population level effects may be observed due to retention dynamics

𝅘𝅥

The dynamic of retention & specialization can lead to representation disparity (Hashimoto et al.) and segmentation [DCRMF23]

Example: linear regression with users      and         

2

1

User Choice & Retention

Even if individual preferences are immutable, population level effects may be observed due to retention dynamics

𝅘𝅥

The dynamic of retention & specialization can lead to representation disparity (Hashimoto et al.) and segmentation [DCRMF23]

Example: linear regression with users      and         

2

1

User Choice & Retention

Even if individual preferences are immutable, population level effects may be observed due to retention dynamics

The dynamic of retention & specialization can lead to representation disparity (Hashimoto et al.) and segmentation [DCRMF23]

Example: linear regression with users      and         

  • services 1 and 2

2

1

  1. Preference Dynamics
  2. Implications: Personalization & Harm
  3. Retention Dynamics

 

  • Behavioral dynamics vs. user agency
  • Network and social dynamics
  • Beyond users: producer and market dynamics

Conclusion & Discussion

  1. Preference Dynamics Under Personalized Recommendations at EC22 (arxiv:2205.13026) with Jamie Morgenstern
  2. Harm Mitigation in Recommender Systems (in submission) with Jerry Chee, Sindhu Ernala, Stratis Ioannidis, Shankar Kalyanaraman, Udi Weinsberg
  3. Emergent segmentation from participation dynamics and multi-learner retraining (in submission, arxiv:2206.02667) with Mihaela Curmei, Lillian J. Ratliff, Jamie Morgenstern, Maryam Fazel

Other References

  • Gaitonde, Kleinberg, Tardos, 2021. Polarization in geometric opinion dynamics. EC.
  • Hązła, Jin, Mossel, Ramnarayan, 2019. A geometric model of opinion polarization. arXiv:1910.05274.
  • Hashimoto, Srivastava, Namkoong, Liang, 2018. Fairness Without Demographics in Repeated Loss Minimization. ICML.

Thanks! Questions?

References

User Dynamics in Machine Learning Systems

By Sarah Dean

User Dynamics in Machine Learning Systems

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