Domain　Generalization　(DG)　aims　to　generalize　a　model　trained　on　multiple　source　domains　to　an　unseen　target　domain.　The　source　domains　always　require　precise　annotations,　which　can　be　cumbersome　or　even　infeasible　to　obtain　in　practice　due　to　the　vast　amount　of　data　involved.　Web　data,　namely　web-crawled　images,　offers　an　opportunity　to　access　large　amounts　of　unlabeled　images　with　rich　style　information,　which　can　be　leveraged　to　improve　DG.　From　this　perspective,　we　introduce　a　novel　paradigm　of　DG,　termed　as　Semi-Supervised　Domain　Generalization　(SSDG),　to　explore　how　the　labeled　and　unlabeled　source　domains　can　interact,　and　establish　two　settings,　including　the　close-set　and　open-set　SSDG.　The　close-set　SSDG　is　based　on　existing　public　DG　datasets,　while　the　open-set　SSDG,　built　on　the　newly-collected　web-crawled　datasets,　presents　a　novel　yet　realistic　challenge　that　pushes　the　limits　of　current　technologies.　A　natural　approach　of　SSDG　is　to　transfer　knowledge　from　labeled　data　to　unlabeled　data　via　pseudo　labeling,　and　train　the　model　on　both　labeled　and　pseudo-labeled　data　for　generalization.　Since　there　are　conflicting　goals　between　domain-oriented　pseudo　labeling　and　out-of-domain　generalization,　we　develop　a　pseudo　labeling　phase　and　a　generalization　phase　independently　for　SSDG.　Unfortunately,　due　to　the　large　domain　gap,　the　pseudo　labels　provided　in　the　pseudo　labeling　phase　inevitably　contain　noise,　which　has　negative　affect　on　the　subsequent　generalization　phase.　Therefore,　to　improve　the　quality　of　pseudo　labels　and　further　enhance　generalizability,　we　propose　a　cyclic　learning　framework　to　encourage　a　positive　feedback　between　these　two　phases,　utilizing　an　evolving　intermediate　domain　that　bridges　the　labeled　and　unlabeled　domains　in　a　curriculum　learning　manner.　Extensive　experiments　are　conducted　to　validate　the　effectiveness　of　our　method.　It　is　worth　highlighting　that　web-crawled　images　can　promote　domain　generalization　as　demonstrated　by　the　experimental　results.　©　2024　Elsevier　Ltd